Taylor Collocation Method for Solving Two dimensional Partial Volterra
We consider a two dimensional partial Volterra integro-differential
equations (PVIDEs). We extend the Taylor collocation method of one
dimensional Volterra integral equations to approximate the solution of
two dimensional partial Volterra integro-differential equations. The
method is based on the use of Taylor polynomials in two dimensional. The
approximate solution is given by using explicit schemes and the method
is proved to be high order convergent with respect to the maximum norm.
Some numerical examples are given to verify the theoretical results.