Galerkin solutions of stiff two-point boundary-value problems

Abstract

Through the example of Conte (Ref. 6), the Galerkin procedure with a small number (N⩽6) of low-degree polynomial modes is illustrated as a computationally rapid and effective technique for solving extremely stiff linear two-point boundary-value problems. Numerical solutions are provided for eigenvalue spreads σ ranging from 20 through 106. They agree with the exact solution to at least 2N decimal places. The errors are insensitive to the eigenvalue spread. Comparisons are made with the continuation technique of Roberts and Shipman (Ref. 1), who did not succeed in solving this example for σ=√(36,000).