Abdulghafor M. Al-Rozbayani and Zeena M. Al-Botani
Subjects
Differential transform method, General Computer Science, General Mathematics, Science, Differential Transform Method, Finite Differences Method, Hybrid Differential Transform - Finite Differences Method, Whitham-Broer-Kaup-Like Equations, Finite difference, General Physics and Astronomy, Applied mathematics, General Chemistry, Agricultural and Biological Sciences (miscellaneous), General Biochemistry, Genetics and Molecular Biology, Mathematics
Abstract
This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.
Caputo derivatives, Fractional Calculus, Fractional Partial differential Equations, Single and double Sumudu , Elzaki transform, 0209 industrial biotechnology, Partial differential equation, General Computer Science, General Mathematics, Science, General Physics and Astronomy, 02 engineering and technology, General Chemistry, 01 natural sciences, Agricultural and Biological Sciences (miscellaneous), General Biochemistry, Genetics and Molecular Biology, Fractional calculus, 010101 applied mathematics, 020901 industrial engineering & automation, Comparison study, Applied mathematics, 0101 mathematics, Mathematics
Abstract
In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using Mathcad 15.and graphic in Matlab R2015a.
General Computer Science, General Mathematics, Science, General Physics and Astronomy, Majorant function, Modified Newton method, Non-linear integral operator, 010103 numerical & computational mathematics, General Chemistry, Function (mathematics), 01 natural sciences, Agricultural and Biological Sciences (miscellaneous), General Biochemistry, Genetics and Molecular Biology, 010101 applied mathematics, Nonlinear system, Operator (computer programming), Applied mathematics, 0101 mathematics, Mathematics
Abstract
In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model. Mathematical Subject Classification (2010): 45P05, 45G10, 47H99
Published
2021
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.