Application of Method of Collocation on Lines for Solving Nonlinear Hyperbolic Problems
Application of Method of Collocation on Lines for Solving Nonlinear Hyperbolic Problems
A collocation on lines procedure based on piecewise polynomials is applied to initial/boundary value problems for nonlinear hyperbolic partial differential equations.Optimal order a priori estimates are obtained for the error of approximation.The Crank-Nicholson discretization in time is studied and convergence rates of the collocation-Crank-Nicholson procedure are established.Finally, the superconvergence is …