Iterative numerical methods for solving partial differential equations. You can find in the Laplace equation with animation notebook an example of solving Laplace equation using Gauss-Seidel iterative ...

The variational iteration method is useful in numerical simulations and approximate analytical solutions, and it is used to resolve nonlinear differential equations in various situations using Maple.

Learn how to find the roots of equations using fixed-point iteration and Newton's method, two common techniques in numerical analysis. Compare their convergence, error, advantages, and disadvantages.

Abstract In this paper, we extend variational iteration method (VIM) to find approximate solutions of linear and nonlinear thirteenth order differential equations in boundary value problems. The ...

Iterative solvers are algorithms that use repeated steps to approximate the solution of a problem, rather than finding the exact solution in one step. For example, if you want to solve a system of ...

However, the existing methods suffer from enormous computational effort. To solve this difficulty, some alternative schemes have been presented including the Adomian decomposition method (ADM) with ...

With the spectral regularities, an N × N rational Toeplitz-plus-Hankel system can be solved by preconditioned iterative methods with O (N log N) operations. Numerical experiments are given to ...

We analyze a heuristic numerical method suggested by V.I. Petviashvili in 1976 for approximation of stationary solutions of nonlinear wave equations. The method is used to construct numerically the ...