Runge–Kutta convolution quadrature methods for well-posed equations with memory |
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Authors: | M P Calvo E Cuesta C Palencia |
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Institution: | (1) Departamento de Matemática Aplicada, Universidad de Valladolid, Valladolid, Spain |
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Abstract: | Runge–Kutta based convolution quadrature methods for abstract, well-posed, linear, and homogeneous Volterra equations, non
necessarily of sectorial type, are developed. A general representation of the numerical solution in terms of the continuous
one is given. The error and stability analysis is based on this representation, which, for the particular case of the backward
Euler method, also shows that the numerical solution inherits some interesting qualitative properties, such as positivity,
of the exact solution. Numerical illustrations are provided. |
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Keywords: | 65J15 65M12 65L05 65M20 |
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