Convergence analysis of structure‐preserving numerical methods for nonlinear Fokker–Planck equations with nonlocal interactions

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

Local convergence analysis of tensor methods for nonlinear equations

Numerical Methods for Nonlinear Estimating Equations

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Convergence analysis of product integration method for nonlinear weakly singular Volterra-Fredholm integral equations

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

Numerical Solution of Some Nonlocal, Nonlinear Dispersive Wave Equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usuall...