Convergence acceleration for boundary value problems with singularities using the E-algorithm

• Published in: Journal of computational and applied mathematics Vol. 61; no. 2; pp. 139 - 164
• Main Authors: Lima, Pedro M., Graça, Mário M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 31.07.1995; Elsevier
• Subjects: Acceleration of convergence; Boundary-value problem; Convergence acceleration; E-algorithm; Exact sciences and technology; Finite-difference method; Green function; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Richardson extrapolation; Sciences and techniques of general use; Trapezoidal rule; Boundary-value problem; Finite-difference method; Convergence acceleration; Trapezoidal rule; Richardson extrapolation; E-algorithm; Green function; Extrapolation; Singularity; Convergence of numerical methods; Boundary value problems; Asymptotic expansion; Differential equations; Trapezoidal method; Approximation error; Green's function; Finite difference method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/0377-0427(94)00065-9

In the present work we use the E-algorithm to accelerate the convergence of finite-difference schemes for ordinary differential equations. As a model, a boundary-value problem for a second-order differential equation is considered, where the right-hand side may have different kinds of singularities. An asymptotic error expansion is obtained, enabling the use of the E-algorithm to accelerate the convergence. The applicability and the efficiency of the E-algorithm are discussed and illustrated by numerical examples.