Pub Date : 2021-01-18DOI: 10.22034/CMDE.2021.36796.1638
Robab Fayyaz Behrouz, M. Amirfakhrian
In this paper, the numerical solution of an algebraic complex fuzzy equation of degree ${n}$, based on the parametric fuzzy numbers, is discussed. The unknown variable and right-hand side of the equation are considered as fuzzy complex numbers, whereas, the coefficients of the equation, are considered to be real crisp numbers. The given method is a numerical method and proposed based on the separation of the real and imaginary parts of the equation and using the parametric forms of the fuzzy numbers in the form of polynomials of degree at most ${m}$. In this case, a system of nonlinear equations achieved. To get the solutions of the system, we used the Gauss-Newton iterative method. We also very briefly explain the conjugate of the solution of such equations. Finally, the efficiency and quality of the given method are tested by applying it to some numerical examples.
{"title":"Numerical Method for the Solution of Algebraic Fuzzy Complex Equations","authors":"Robab Fayyaz Behrouz, M. Amirfakhrian","doi":"10.22034/CMDE.2021.36796.1638","DOIUrl":"https://doi.org/10.22034/CMDE.2021.36796.1638","url":null,"abstract":"In this paper, the numerical solution of an algebraic complex fuzzy equation of degree ${n}$, based on the parametric fuzzy numbers, is discussed. The unknown variable and right-hand side of the equation are considered as fuzzy complex numbers, whereas, the coefficients of the equation, are considered to be real crisp numbers. The given method is a numerical method and proposed based on the separation of the real and imaginary parts of the equation and using the parametric forms of the fuzzy numbers in the form of polynomials of degree at most ${m}$. In this case, a system of nonlinear equations achieved. To get the solutions of the system, we used the Gauss-Newton iterative method. We also very briefly explain the conjugate of the solution of such equations. Finally, the efficiency and quality of the given method are tested by applying it to some numerical examples.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46518286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-18DOI: 10.22034/CMDE.2021.39703.1739
N. Iftikhar, S. T. Saeed, M. Riaz
This study explores the time-dependent convective flow of MHD Oldroyd-B fluid under the effect of ramped wall velocity and temperature. The flow is confined to an infinite vertical plate embedded in a permeable surface with the impact of heat generation and thermal radiation. Solutions of velocity, temperature, and concentration are derived symmetrically by applying non-dimensional parameters along with Laplace transformation $(LT)$ and numerical inversion algorithm. Graphical results for different physical constraints are produced for the velocity, temperature, and concentration profiles. Velocity and temperature profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Velocity is decreasing for $kappa$, $M$, $Pr_{reff,}$ and $Sc$ while increasing for $G_{r}$ and $G_{c}$. Temperature is an increasing function of the fractional parameter. Additionally, Atangana-Baleanu $(ABC)$ model is good to explain the dynamics of fluid with better memory effect as compared to other fractional operators.
{"title":"Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature","authors":"N. Iftikhar, S. T. Saeed, M. Riaz","doi":"10.22034/CMDE.2021.39703.1739","DOIUrl":"https://doi.org/10.22034/CMDE.2021.39703.1739","url":null,"abstract":"This study explores the time-dependent convective flow of MHD Oldroyd-B fluid under the effect of ramped wall velocity and temperature. The flow is confined to an infinite vertical plate embedded in a permeable surface with the impact of heat generation and thermal radiation. Solutions of velocity, temperature, and concentration are derived symmetrically by applying non-dimensional parameters along with Laplace transformation $(LT)$ and numerical inversion algorithm. Graphical results for different physical constraints are produced for the velocity, temperature, and concentration profiles. Velocity and temperature profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Velocity is decreasing for $kappa$, $M$, $Pr_{reff,}$ and $Sc$ while increasing for $G_{r}$ and $G_{c}$. Temperature is an increasing function of the fractional parameter. Additionally, Atangana-Baleanu $(ABC)$ model is good to explain the dynamics of fluid with better memory effect as compared to other fractional operators.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46724467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.40684.1772
H. Budak, Hasan Kara, Rabia Kapucu
In this paper, we first establish two new identities for differentiable function involving generalized fractional integrals. Then, by utilizing these equalities, we obtain some midpoint type inequalities involving generalized fractional integrals for mappings whose derivatives in absolute values are convex. We also give several results as special cases of our main results.
{"title":"New midpoint type inequalities for generalized fractional integral","authors":"H. Budak, Hasan Kara, Rabia Kapucu","doi":"10.22034/CMDE.2020.40684.1772","DOIUrl":"https://doi.org/10.22034/CMDE.2020.40684.1772","url":null,"abstract":"In this paper, we first establish two new identities for differentiable function involving generalized fractional integrals. Then, by utilizing these equalities, we obtain some midpoint type inequalities involving generalized fractional integrals for mappings whose derivatives in absolute values are convex. We also give several results as special cases of our main results.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44389903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.40112.1749
M. Zarebnia, R. Parvaz
In this work, collocation method based on B-spline functions is used to obtained a numerical solution for one-dimensional hyperbolic telegraph equation. The proposed method is consists of two main steps. As first step, by using finite difference scheme for time variable, partial differential equation is converted to an ordinary differential equation by space variable. In the next step, for solving this equation collocation method is used. In the analysis section of the proposed method, the convergence of the method is studied. Also, some numerical results are given to demonstrate the validity and applicability of the presented technique. The L∞, L2 and Root-Mean-Square(RMS) in the solutions show the efficiency of the method computationally.
{"title":"An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic b-spline functions","authors":"M. Zarebnia, R. Parvaz","doi":"10.22034/CMDE.2020.40112.1749","DOIUrl":"https://doi.org/10.22034/CMDE.2020.40112.1749","url":null,"abstract":"In this work, collocation method based on B-spline functions is used to obtained a numerical solution for one-dimensional hyperbolic telegraph equation. The proposed method is consists of two main steps. As first step, by using finite difference scheme for time variable, partial differential equation is converted to an ordinary differential equation by space variable. In the next step, for solving this equation collocation method is used. In the analysis section of the proposed method, the convergence of the method is studied. Also, some numerical results are given to demonstrate the validity and applicability of the presented technique. The L∞, L2 and Root-Mean-Square(RMS) in the solutions show the efficiency of the method computationally.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41461454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.39472.1726
Swarn Singh, S. Bhatt, Suruchi Singh
In this paper, an approximate solution of non-linear parabolic partial differential equation is obtained for a non-uniform mesh. The scheme for partial differential equation subject to Neumann boundary is based on cubic B-spline collocation method. Modified cubic B-splines are proposed over non-uniform mesh to deal with the Dirichlet boundary conditions. This scheme produces a system of first order ordinary differential equations. This system is solved by Crank Nicholson method. The stability is also discussed using Von Neumann stability analysis. The accuracy and efficiency of the scheme is shown by numerical experiments. We have compared the approximate solutions with that in the literature.
{"title":"Cubic B-spline collocation method on non-uniform mesh for solving non-linear parabolic partial differential equation","authors":"Swarn Singh, S. Bhatt, Suruchi Singh","doi":"10.22034/CMDE.2020.39472.1726","DOIUrl":"https://doi.org/10.22034/CMDE.2020.39472.1726","url":null,"abstract":"In this paper, an approximate solution of non-linear parabolic partial differential equation is obtained for a non-uniform mesh. The scheme for partial differential equation subject to Neumann boundary is based on cubic B-spline collocation method. Modified cubic B-splines are proposed over non-uniform mesh to deal with the Dirichlet boundary conditions. This scheme produces a system of first order ordinary differential equations. This system is solved by Crank Nicholson method. The stability is also discussed using Von Neumann stability analysis. The accuracy and efficiency of the scheme is shown by numerical experiments. We have compared the approximate solutions with that in the literature.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48154397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.29281.1411
Z. Soltani
In this paper, we prove the existence of solution of two nonlinear integral inclusions by using generalization of Krasnoselskii fixed point theorem for set-valued mappings. As an application we prove the existence of solution of the boundary valued problem of ordinary differential inclusion.
{"title":"Existence of solution for nonlinear integral inclusions","authors":"Z. Soltani","doi":"10.22034/CMDE.2020.29281.1411","DOIUrl":"https://doi.org/10.22034/CMDE.2020.29281.1411","url":null,"abstract":"In this paper, we prove the existence of solution of two nonlinear integral inclusions by using generalization of Krasnoselskii fixed point theorem for set-valued mappings. As an application we prove the existence of solution of the boundary valued problem of ordinary differential inclusion.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47095602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.41241.1792
R. Kazemi, M. H. Akrami
In this paper, we study the monotonicity and convexity of the period function associated with centers of a specific class of symmetric Newtonian systems of degree 8. In this regard, we prove that if the period annulus surrounds only one elementary center, then the corresponding period function is monotone; but, for the other cases, the period function has exactly one critical point. We also prove that in all cases, the period function is convex.
{"title":"The monotonicity and convexity of the period function for a class of symmetric Newtonian systems of degree 8","authors":"R. Kazemi, M. H. Akrami","doi":"10.22034/CMDE.2020.41241.1792","DOIUrl":"https://doi.org/10.22034/CMDE.2020.41241.1792","url":null,"abstract":"In this paper, we study the monotonicity and convexity of the period function associated with centers of a specific class of symmetric Newtonian systems of degree 8. In this regard, we prove that if the period annulus surrounds only one elementary center, then the corresponding period function is monotone; but, for the other cases, the period function has exactly one critical point. We also prove that in all cases, the period function is convex.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42429793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.38990.1711
T. Sulaiman, U. Younas, M. Younis, J. Ahmad, S. Rehman, M. Bilal, A. Yusuf
The current study utilizes the extended sinh-Gordon equation expansion and ($frac{G^{prime}}{G^2}$)-expansion function methods in constructing various optical soliton and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schr${ddot o}$dinger's equation which describes the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics. We secure different kinds of solutions like optical dark, bright, singular, combo solitons as well as hyperbolic and trigonometric functions solutions. Moreover, singular periodic wave solutions are recovered and the constraint conditions which provide the guarantee to the soliton solutions are also reported. In order to shed more light on these novel solutions, graphical features 3D, 2D and contour with some suitable choice of parameter values have been depicted. We also discuss the stability analysis of the studied nonlinear model with aid of modulation instability analysis.
{"title":"Modulation instability analysis, optical solitons and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schrodinger's equation","authors":"T. Sulaiman, U. Younas, M. Younis, J. Ahmad, S. Rehman, M. Bilal, A. Yusuf","doi":"10.22034/CMDE.2020.38990.1711","DOIUrl":"https://doi.org/10.22034/CMDE.2020.38990.1711","url":null,"abstract":"The current study utilizes the extended sinh-Gordon equation expansion and ($frac{G^{prime}}{G^2}$)-expansion function methods in constructing various optical soliton and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schr${ddot o}$dinger's equation which describes the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics. We secure different kinds of solutions like optical dark, bright, singular, combo solitons as well as hyperbolic and trigonometric functions solutions. Moreover, singular periodic wave solutions are recovered and the constraint conditions which provide the guarantee to the soliton solutions are also reported. In order to shed more light on these novel solutions, graphical features 3D, 2D and contour with some suitable choice of parameter values have been depicted. We also discuss the stability analysis of the studied nonlinear model with aid of modulation instability analysis.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46127191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.41858.1812
H. R. Ghehsareh, M. Seidzadeh, Seyed Kamal Etesami
Medical ultrasound images are usually degraded by a specific type of noise, called "speckle". The presence of speckle noise in medical ultrasound images will reduce the image quality and affect the effective information, which can potentially cause a misdiagnosis. Therefore, medical image enhancement processing has been extensively studied and several denoising approaches have been introduced and developed. In the current work, a robust fractional partial differential equation (FPDE) model based on the anomalous diffusion theory is proposed and used for medical ultrasound image enhancement. An efficient computational approach based on a combination of a time integration scheme and localized meshless method in a domain decomposition framework is performed to deal with the model. {In order to evaluate the performance of the proposed de-speckling approach, it is used for speckle noise reduction of a synthetic ultrasound image degraded by different levels of speckle noise. The results indicate the superiority of the proposed approach in comparison with classical anisotropic diffusion denoising model (Catt$acute{e}$'s pde model).}
{"title":"An Anomalous Diffusion Approach for Speckle Noise Reduction in Medical Ultrasound Images","authors":"H. R. Ghehsareh, M. Seidzadeh, Seyed Kamal Etesami","doi":"10.22034/CMDE.2020.41858.1812","DOIUrl":"https://doi.org/10.22034/CMDE.2020.41858.1812","url":null,"abstract":"Medical ultrasound images are usually degraded by a specific type of noise, called \"speckle\". The presence of speckle noise in medical ultrasound images will reduce the image quality and affect the effective information, which can potentially cause a misdiagnosis. Therefore, medical image enhancement processing has been extensively studied and several denoising approaches have been introduced and developed. In the current work, a robust fractional partial differential equation (FPDE) model based on the anomalous diffusion theory is proposed and used for medical ultrasound image enhancement. An efficient computational approach based on a combination of a time integration scheme and localized meshless method in a domain decomposition framework is performed to deal with the model. {In order to evaluate the performance of the proposed de-speckling approach, it is used for speckle noise reduction of a synthetic ultrasound image degraded by different levels of speckle noise. The results indicate the superiority of the proposed approach in comparison with classical anisotropic diffusion denoising model (Catt$acute{e}$'s pde model).}","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42292367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-05DOI: 10.22034/CMDE.2020.37370.1670
O. Baghani, S. Harikrishnan, K. Kanagarajan
We discuss successive approximation techniques for the investigation of solutions of fractional differential equations with $psi$-Hilfer fractional derivative. Next, we present the continuous dependence of a solution for the given Cauchy-type problem.
{"title":"Qualitative analysis of fractional differential equations with $psi$-Hilfer fractional derivative","authors":"O. Baghani, S. Harikrishnan, K. Kanagarajan","doi":"10.22034/CMDE.2020.37370.1670","DOIUrl":"https://doi.org/10.22034/CMDE.2020.37370.1670","url":null,"abstract":"We discuss successive approximation techniques for the investigation of solutions of fractional differential equations with $psi$-Hilfer fractional derivative. Next, we present the continuous dependence of a solution for the given Cauchy-type problem.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45976398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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