Discrete Galerkin and related onestep methods for ordinary differential equations
Author:
Bernie L. Hulme
Journal:
Math. Comp. 26 (1972), 881891
MSC:
Primary 65L05
MathSciNet review:
0315899
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Abstract: New techniques for numerically solving systems of firstorder 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:
http://dx.doi.org/10.1090/S00255718197203158998
PII:
S 00255718(1972)03158998
Keywords:
Discrete Galerkin methods,
initial value problems,
ordinary differential equations,
piecewise polynomials,
collocation,
quadrature,
implicit RungeKutta methods,
stable
Article copyright:
© Copyright 1972 American Mathematical Society
