Journal of Mathematical Chemistry最新文献

In this paper, we discuss an efficient numerical method to obtain all solutions of fractional Gelfand equation with Dirichlet boundary condition. More precisely, we derive a good initial value motivated by the bifurcation curve of fractional Gelfand equation. It is obvious to see that the number of solutions depends on the value of parameter in fractional Gelfand equation. By collocation technique and finite difference method, numerical solutions can be found very quickly based on Newton iteration method with the aid of such initial guess. Numerical simulation for one-dimensional fractional Gelfand equation are provided, which demonstrates the accuracy and easy-to-implement of our algorithm.

The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a property that is relevant in the decision-making of cells. Determining which reaction rate constants correspond to monostationarity and which produce multistationarity is an open problem. The system’s monostationarity is linked to the nonnegativity of a specific polynomial. A previous study by Feliu et al. provides a sufficient condition for monostationarity via a decomposition of this polynomial into nonnegative circuit polynomials. However, this decomposition is not unique. We extend their work by a systematic approach to classifying such decompositions in the dual phosphorylation network. Using this classification, we provide a qualitative comparison of the decompositions into nonnegative circuit polynomials via empirical experiments and improve on previous conditions for the region of monostationarity.

This paper investigates a higher-order numerical technique for solving an inhomogeneous time fractional reaction-advection-diffusion equation with a nonlocal condition. The time-fractional operator involved here is the Caputo derivative. We discretize the Caputo derivative by an L1–2 formula, while the compact finite difference scheme approximates the spatial derivatives. The numerical approach is based on Taylor’s expansion combined with modified Gauss elimination. A thorough study demonstrates that the suggested approach is unconditionally stable. Tabular results show that the proposed scheme has fourth-order accuracy in space and ((3-beta ))-th-order accuracy in time. The numerical results of two test problems demonstrate the effectiveness and reliability of the theoretical estimates.

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.