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, …