Deferred Correction Methods for Initial Boundary Value Problems
Copyright policy )Deferred Correction Methods for Initial Boundary Value Problems
The numerical solution of the linear problem \[ {\partial u\over\partial t}={\mathcal P}(u)+ F(x,t),\quad u(x,0)= f(x) \] with appropriate boundary conditions by the method of lines gives rise to a large system of ordinary differential equations. The purpose of the paper is to apply the deferred correction principle to this system with initial conditions. The paper contains a proof of a stability estimate for a special case of time dependent coefficients as well as error estimates. It concludes with some numerical experiments.
- Uppsala University Sweden
Method of lines for initial value and initial-boundary value problems involving PDEs, convergence, initial boundary value problems, implicit difference methods, method of lines, deferred correction, stability, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, high-order methods, Nonlinear parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, numerical experiments
Method of lines for initial value and initial-boundary value problems involving PDEs, convergence, initial boundary value problems, implicit difference methods, method of lines, deferred correction, stability, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, high-order methods, Nonlinear parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, numerical experiments
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