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

Document Type : Full Length Article


Qazvin Branch, Islamic Azad University


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