Numerical Solution for Semi Linear Hyperbolic Differential Equations

A Numerical method is proposed for the solution of semi linear hyperbolic differential equation. The method is of the characteristic type and it is particularly helpful in case of discontinuous initial data. The new proposal is elaborated and implemented in Matlab for canonical case of differential equation. Then, its local and global order of convergence is conventionally estimated using canonical examples. The method is extended for the solution of a wave equation with a non-classical right boundary condition, where special treatment of the right boundary is required.