Discrete Galerkin and related one-step methods for ordinary differential equations

Author:
Bernie L. Hulme

Journal:
Math. Comp. **26** (1972), 881-891

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1972-0315899-8

MathSciNet review:
0315899

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Abstract | References | Similar Articles | Additional Information

Abstract: New techniques for numerically solving systems of first-order ordinary differential equations are obtained by finding local Galerkin approximations on each subinterval of a given mesh. Different classes of methods correspond to different quadrature rules used to evaluate the innerproducts involved. At each step, a polynomial of degree is constructed and the arcs are joined together continuously, but not smoothly, to form a piecewise polynomial of degree and class . If the -point quadrature rule used for the innerproducts is of order , then the Galerkin method is of order at the mesh points. In between the mesh points, the th derivatives have accuracy of order , for and for .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0315899-8

Keywords:
Discrete Galerkin methods,
initial value problems,
ordinary differential equations,
piecewise polynomials,
collocation,
quadrature,
implicit Runge-Kutta methods,
-stable

Article copyright:
© Copyright 1972
American Mathematical Society