Numerical Solution of The First-Order Evolution Equations by Radial Basis Function

Abstract

‎In this work‎, ‎we consider the nonlinear first-order evolution‎<br /> ‎equations‎: ‎$u_t=f(x,t,u,u_x,u_{xx})$ for $0<t<infty$‎, ‎subject‎<br /> ‎to initial condition $u(x,0)=g(x)$‎, ‎where $u$ is a function of‎<br /> ‎$x$ and $t$ and $f$ is a known analytic function‎. ‎The purpose of‎<br /> ‎this paper is to introduce the method of RBF to existing method‎<br /> ‎in solving nonlinear first-order evolution equations and also the‎ ‎method is implemented in four numerical examples‎. ‎The results‎<br /> ‎reveal that the technique is very effective and simple.