Journal of Mathematical Chemistry最新文献

This study focuses on crafting and examining the high-order numerical technique for the two-dimensional time-fractional Burgers equation(2D-TFBE) arising in modelling of polymer solution. The time derivative of order ({alpha }) in the equation (where (alpha in (0,1))) is approximated using the fast scheme, while space derivatives are discretized via a tailored finite point formula (TFPF) which relies on exponential basis. This method uses exponential functions to simultaneously fit the local solution’s properties in time and space, serving as basis functions within the TFPF framework. The analysis of convergence and stability of the method are rigorously examined theoretically and these are supported by the numerical examples showcasing its applicability and accuracy. It is proven that the method is unconditionally stable and maintains an accuracy of order ({mathcal {O}}(tau ^2+h_{varkappa }+h_y+epsilon + varepsilon ^{-2}e^{-frac{beta _{n,m}^{k+1}}{2varepsilon ^2}}+e^{-gamma _0frac{h}{varepsilon }} )), where (tau ) represents the temporal step size, and (h_{varkappa }) and (h_y) are spatial step sizes. Computational outcomes align well with the theoretical analysis. Furthermore, when compared to the standard scheme, our method attains the same level of accuracy with significantly lowering computational demands and minimizing storage requirements. This proposed numerical scheme has higher convergence rate and significantly minimizes consumed CPU time compared to other methods.

A family of new exponentially fitted two-derivative Runge–Kutta (TDRK) methods with exponential order up to two for solving the Schrödinger equation is obtained in this paper. Error analysis is conducted in terms of the asymptotic expressions of the energy. Linear stability and phase properties are analyzed. Numerical results are reported to show the efficiency and robustness of the new methods in comparison with some RK type methods specially tuned to the integration of the radial time-independent Schrödinger equation with the Woods-Saxon potential.

The parameter optimization for microwave-assisted simultaneous distillation and extraction (MA-SDE) was performed using Response Surface Methodology (RSM) to enhance the yield of essential oil from Pluchea indica (Khlu in Thai) leaf tea. Two design approaches, Box-Behnken Design (BBD) and Face Central Composite Design (FCCD), were compared for their effectiveness in modeling and optimizing the MA-SDE process. A quadratic polynomial model was identified as optimal for essential oil extraction through correlation analysis of the mathematical regression models. The response model is supported by the high degree of agreement between predicted and actual responses observed in both models, with a residual standard error (RSE) of less than 5%. The regression quadratic MA-SDE models developed showed R² values of 0.832 for FCCD and 0.951 for BBD, with the BBD model demonstrating superior performance due to its higher R² value. Additionally, BBD required significantly fewer experiments, making it more efficient in terms of resource and time utilization than FCCD. As a result, BBD is recommended as the preferred approach for optimizing essential oil extraction from Pluchea indica leaf tea using MA-SDE.

In Roul and Warbhe (2016) J. Comp. Appl. Math. 296: 661–676, Roul and Warbhe proposed a computational technique for solving a class of doubly singular boundary value problems (DSBVP). This method approximates the solution of DSBVP in the form of a series but requires a large number of components in the series to achieve a reasonably good accuracy. In this paper, a fast and computationally efficient approach is introduced to approximate the solution to the same DSBVP. Additionally, convergence of the suggested scheme is rigorously proven. Two test problems are considered to demonstrate the efficiency and accuracy of the method. Comparison is performed between the proposed method and the method in Roul and Warbhe (2016) J. Comp. Appl. Math. 296: 661–676. The execution time of the present method is provided.

In this paper, we introduce an economical technique based on a semi-implicit predictor–corrector scheme for solving fractional Benjamin–Bona–Mahony–Burgers equations, in which the Adams–Moulton schemes are used for predictor and corrector schemes. To resolve a nonlinearity of the given equations in the predictor procedure, the weighted Rubin–Graves linearization scheme is applied to convert the linearized equations at the predictor procedure. Moreover, to alleviate weak regularity at the initial time point, mixed meshes based on uniform grid are used so that it can save the computational costs by not recalculating the coefficients of Adams–Moulton methods for smaller time intervals. The convergence analysis are analytically executed to derive the convergence order and are numerically supported. Several numerical results are provided to show the efficiency of the proposed scheme.

The thermodynamic properties of bilayer graphene under dual gating have been studied as a function of temperature in the presence of an external perpendicular magnetic field. AB-stacked bilayer graphene quantum dots are investigated, and the energy levels are determined both without and with an applied magnetic field. Numerical expressions for mean energy, specific heat, magnetization, entropy, and susceptibility are calculated using the partition function. Specific heat showed a peak in the presence of a magnetic field, while magnetic susceptibility exhibited positive values in region 2, influenced by Landau levels and magnetic field effects.

The Thomas equation, which controls ion exchange as well as chemical kinetics and advection processes in chemical systems, has its coefficients expanded as functions of time in this work. The goal of this modification is to produce simulations of advection and kinetic processes that are more precise and lifelike. In order to examine the nonlinear distribution and interaction features, the dynamic traveling wave solution of the time-dependent variable coefficient Thomas equation has been successfully achieved. The physical properties of the constants and functions in the wave model presented with certain initial and boundary conditions have been examined. Constants and functions are designed to be as close to reality as possible in order to improve our understanding of the distribution of ions over time in the chemical process. With this design, the newly introduced dynamic traveling wave model is better adapted to the ion exchange process. The coefficient functions that have a direct effect on the stability of the physical mechanism are analyzed under which conditions the system will remain stable. It is envisaged that ion exchange processes in water treatment plants can be optimized by using the wave model introduced for the first time in this study. The gradual damping of ion motions in the chemical process and the trend towards equilibrium over time were investigated using the proposed model.

This investigation focuses on the unsteady three-dimensional electrically conducting nanofluid flow over a bilateral nonlinear stretching sheet. A novel mathematical model is developed to incorporate the influences of Arrhenius activation energy, nonlinear thermal radiation, and Joule heating. The Taylor wavelet series collocation method (TWSCM) is employed for analysis. The governing partial differential equations (PDEs) are transformed by applying suitable similarity transformation into nonlinear coupled ordinary differential equations (ODEs). These ODEs are then solved using the TWSCM approach. This method allows us to explore how various physical parameters influence mass and heat transfer in the nanofluid flow. The findings reveal that the thermal Biot number and activation energy parameter significantly enhance the concentration field. Moreover, the heat transfer rate is found to increase with the temperature ratio and thermal Biot parameters while decreasing with the activation energy parameter.