New approach on conventional solutions to nonlinear partial differential equations describing physical phenomena

•New Approach on Conventional Solutionsto Nonlinear Partial Differential Equations.•Numerical treatment of different types of diffusion and convection–diffusion equations.•A supplementary parameter which guarantees a faster convergence rate is presented.•Comparison with compact finite-difference met...

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Veröffentlicht in:Results in physics Jg. 41; S. 105936
Hauptverfasser: Ahmad, Hijaz, Khan, Tufail A., Stanimirovic, Predrag S., Shatanawi, Wasfi, Botmart, Thongchai
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.10.2022
Elsevier
Schlagworte:
Convection–diffusion equation
Diffusion equation
Modified variational iteration algorithm-I
Physical phenomena
Convection–diffusion equation
Modified variational iteration algorithm-I
Diffusion equation
Physical phenomena
ISSN:2211-3797, 2211-3797
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Zusammenfassung:•New Approach on Conventional Solutionsto Nonlinear Partial Differential Equations.•Numerical treatment of different types of diffusion and convection–diffusion equations.•A supplementary parameter which guarantees a faster convergence rate is presented.•Comparison with compact finite-difference method and the second kind Chebyshev wavelets to show the efficiency, precision and implementation of the method.•The proposed algorithm is considered as a very good technique for solving practical problems resulting in different fields of applied physical sciences and engineering. In current study, the modified variational iteration algorithm-I is investigated in the form of the analytical and numerical treatment of different types of nonlinear partial differential equations modelling physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. In this modified algorithm, a supplementary parameter which guarantees a faster convergence rate is presented. Appropriate values of the additional parameter are obtained after minimization of properly defined error functions. The obtained results are compared against the exact solutions as well as against numerical solutions generated by the compact finite-difference method, fourth-order finite difference scheme, the second kind Chebyshev wavelets, DQ Chebyshev, and DQ Lagrange methods to show the efficiency, precision and implementation of the method. The proposed algorithm is considered as a very good technique for solving practical problems resulting in different fields of applied physical sciences and engineering.
ISSN:2211-3797
2211-3797
DOI:10.1016/j.rinp.2022.105936