Variable-step boundary value methods based on reverse Adams schemes and their grid redistribution Original Research Article

The variable-step boundary value methods based on reverse k-step Adams schemes are defined for the solution of initial value problems. The paper discusses attainable convergence orders, conditioning of resulting discretization matrices and introduces a grid redistribution strategy based on equidistribution of the local truncation error. An adaptive algorithm is tested on several linear and nonlinear examples and the results strongly support the theory. The method is suitable for a parallel solution of stiff initial value problems.