Invariant Imbedding and the Solution of Fredholm Integral Equations with Displacement Kernels -- Comparative Numerical Experiments,
RAND CORP SANTA MONICA CALIF
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Some recent literature has dealt with problems of numerical solution of certain types of Fredholm integral equations by replacing them with initial value problems for a system of ordinary differential equations which also contain integrals of the unknown functions with respect to a parameter method of invariant imbedding. However, no experiments have heretofore been carried out to test the relative efficiencies of the invariant imbedding method vis-a-vis traditional solution techniques. In this paper the results of such a numerical experiment are described. The experiment consists in comparing the methods of invariant imbedding, successive approximations Picard method, linear algebraic equations, and Sokolovs method of averaging functional corrections to solve numerically two representatives of a class of Fredholm integral equations.
- Theoretical Mathematics