Method of lines for pseudoparabolic equations
We consider initial-boundary-value problems for a class of pseudoparabolic partial differential equations. Local-in-time existence results and nonexistence of global-in-time solutions are proved. We apply the method of lines to approximate pseudoparabolic equations by systems of ordinary differential equations. We present a complete convergence analysis for this semidiscretization method. Blow-up for approximate solutions is showed. Numerical experiments confirm the theoretical results.