Finite Difference Approximations for a Class of Semilinear Volterra Evolution Problems
Author:
- Lucio TaverniniLTLucio Tavernini
- 1 October 1977
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 14 (5) , 931-949
Abstract
This paper deals with the numerical integration of some initial and initial-boundary value problems in partial differential equations where the derivatives may depend on the history of the solution by the inclusion of certain “memory” terms. An abstract trapezoidal rule is presented and a detailed error analysis of the order of convergence is given. Two order of convergence theorems are developed which predict the correct fractional order of convergence for solutions of low continuity with respect to the time variable.Keywords
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