Spline collocation method of lines for solution of linear and nonlinear parabolic and hyperbolic differential equations with nonlocal boundary conditions. (submited)
Abstract
In this paper, we consider the problem of solving the one-dimensional linear and nonlinear parabolic and hyperbolic partial differential equations subject to given initial and non-local boundary conditions. The approximate solution is found using the method of lines (MOL). The MOL converts a partial differential equation to a system of ordinary differential equations. The partial derivatives with respect to the space variable are discretized by spline collocation method. Numerical results are presented to compare the method of this paper with some existing methods.