In this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the obtained results demonstrate reliability and activity of the proposed technique. This strategy gives a precise and productive system in comparison with other traditional techniques and the arrangements methodology is extremely straightforward and few emphasis prompts high exact solution. The numerical outcomes showed that the acquired estimated solutions were in appropriate concurrence with the correct solution.

This paper describes a procedure which combines between the Wilkinson and Aitken methods in order to obtain a best approximation of the greatest eigenvalue. Both the symmetric and the nonsymmetric matrices are solved. It shows that our suggested method converges quickly and it is quit insensitive to the properties of the matrices used. A comparison between these approximations for five numerical examples is given, depending on the number of iterations and running computer time. Experimental results indicate that the new numerical procedure is more efficient than Power, Wilkinson and Aitken methods.

In this article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredholm integro-differential equations of higher-order. Illustrations are used to test the technique’s accuracy and validity. Comparison among the acquired consequences by EDM and actual solutions have proven the power and accuracy of this technique. This technique is dependable and able to supply analytic remedies for solving such equations.

This paper deals with approximation solution for coupled of space-time-fractional of both the equal width wave equation(FCEWE) and the modified equal width wave equation (FCMEWE) using Bernstein polynomials with collocation method and employing the Caputo definition for fractional derivatives. The method reduces the coupled system to a system of algebraic equations which is simple in handling and gives the best results.

Anon-linear parabolic system is derived to describe incompressible nuclear waste disposal contamination in porous media. Galerkin method is applied for the pressure equation. For