An efficient error analysis solutions of fractional pseudo-parabolic partial differential equations via the Dufort-Frankel method

jargess Abdulla; Raveen Fawzi  Taher

doi:10.5269/bspm.76345

jargess Abdulla University of Duhok
Raveen Fawzi Taher University of Duhok

Abstract

This paper presents a numerical approach for solving pseudo-parabolic partial differential equations using the Dufort-Frankel difference scheme. The method is applied to a fractional-order initial boundary value problem, and stability estimates are derived for the proposed scheme. Error analysis is conducted by comparing exact and approximate solutions, demonstrating the effectiveness of the method. The results indicate that the Dufort-Frankel scheme is well-suited for solving these problems.

Downloads

Download data is not yet available.

Author Biography

Raveen Fawzi Taher, University of Duhok

Department of Mathematics, College of Basic Education, University of Duhok, Duhok, Iraq

References

Abdulazeez, S. T., Modanli, M., Solutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method, Alexandria Engineering Journal 61, 12443-12451, (2022).

Xie, B., Gao, Y., Numerical Analysis for Fractional Riccati Differential Equations Based on Finite Difference Method, Journal of Nonlinear Modeling and Analysis 7(1), 189-208, (2025).

Modanli, M., Abdulazeez, S. T., Husien, A. M., A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions, Numerical Methods for Partial Differential Equations 37, 2235-2243, (2021).

Abdulazeez, S. T., Modanli, M., Husien, A. M., Solutions to nonlinear pseudo hyperbolic partial differential equations with nonlocal conditions by using residual power series method, Sigma 41, 488-492, (2023).

Patra, A., Pasayat, T., Travelling Wave Solution for Generalised (4+1) Dimensional Fractional Order Fokas Equation Using Residual Power Series method, International Journal of Theoretical Physics 64(2), 1-16, (2025).

Abdulazeez, S. T., Modanli, M., Husien, A. M., Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations, Journal of Applied Mathematics and Computational Mechanics 21, (2022).

Abdulla, S. O., Abdulazeez, S. T., Modanli, M., Comparison of third-order fractional partial differential equation based on the fractional operators using the explicit finite difference method, Alexandria Engineering Journal 70, 37-44, (2023).

Modanli, M., Abdulazeez, S. T., Akgul, A., Explicit Finite Difference Analysis of Pseudo-Hyperbolic Partial Differential Equations, (2022).

Abu Arqub, O., Application of residual power series method for the solution of time-fractional Schrodinger equations in one-dimensional space, Fundamenta Informaticae 166, 87-110, (2019).

Kumar, A., Kumar, S., Yan, S. P., Residual power series method for fractional diffusion equations, Fundamenta Informaticae 151, 213-230, (2017).

Murad, M. A. S., Hamadamen, M. H., Abdulazeez, S. T., Modified Computational Method Based on Integral Transform for Solving Fractional Zakharov-Kuznetsov Equations, Matrix Science Mathematic (MSMK) 7, 01-06, (2023).

Modanli, M., Murad, M. A. S., Abdulazeez, S. T., A new computational method-based integral transform for solving time-fractional equation arises in electromagnetic waves, Zeitschrift fur angewandte Mathematik und Physik 74, 186, (2023).

Mesloub, S., A nonlinear nonlocal mixed problem for a second order pseudoparabolic equation, Journal of mathematical analysis and applications 316, 189-209, (2006).

Dehghan, M., Hamidi, A., Shakourifar, M., The solution of coupled Burgers’ equations using Adomian-Pade technique, Applied Mathematics and Computation 189, 1034-1047, (2007).

Bakodah, H. O., Al-Harbi, R. M., Alshareef, A., Alshaery, A. A., A New Computational Method Based on the Method of Lines and Adomian Decomposition Method for Burgers’ Equation and Coupled System of Burgers’ Equations, International Journal of Analysis and Applications 23, 44, (2025).

Aminikhah, H., An analytical approximation for coupled viscous Burgers’ equation, Applied Mathematical Modelling 37, 5979-5983, (2013).

Gadain, H. E., Solving coupled pseudo-parabolic equation using a modified double Laplace decomposition method, Acta Mathematica Scientia 38, 333-346, (2018).

Yadav, S., Pandey, R. K., Numerical approximation of fractional Burgers equation with Atangana-Baleanu derivative in Caputo sense, Chaos, Solitons Fractals 133, 109630, (2020).

Li, C., Chen, A., Numerical methods for fractional partial differential equations, International Journal of Computer Mathematics 95, 1048-1099, (2018).

Jachimaviˇcien˙e, J., Sapagovas, M., ˇStikonas, A., ˇStikonien˙e, O., On the stability of explicit finite difference schemes for a pseudoparabolic equation with nonlocal conditions, Nonlinear analysis: modelling and control 19, 225-240, (2014).

Sun, F., Liu, L., Wu, Y., Finite time blow-up for a class of parabolic or pseudo-parabolic equations, Computers Mathematics with Applications 75, 3685-3701, (2018).

Ozba˘g, F., Modanli, M., Abdulazeez, S. T., Numerical Solutions for Mixed Fractional Order Two-Dimensional Telegraph Equations, Bitlis Eren Universitesi Fen Bilimleri Dergisi 13, 1023-1030, (2024).

Ibrahim, G. O., Taiwo, A. O., Modified Laplace-Adomian Decomposition Method for Solving System of Fractional Partial Differential Equations, Journal of Institutional Research, Big Data Analytics and Innovation 1(2), 84-93, (2025).

Modanli, M., Abdulazeez, S. T., Husien, A. M., A new approach for pseudo hyperbolic partial differential equations with nonLocal conditions using Laplace Adomian decomposition method, Applied Mathematics-A Journal of Chinese Universities 39, 750-758, (2024).