Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences · 1953 · 188 citations · 4 references
Abstract The integral equations discussed and illustrated are those of Fredholm, with fixed limits in the integral and including the eigenvalue problem, and of Volterra, with a variable upper limit in the integral. The methods are mostly based on finite-difference theory, the integrals being replaced by formulae for numerical quadrature. Computational details are given for several methods, and there is a discussion of error analysis for Volterra’s equation. Some methods are given for accelerating the convergence of classical iterative processes.
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