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The spectral methods for parabolic Volterra integro-differential equations. (English) Zbl 1219.65161

Summary: We study the numerical solutions to parabolic Volterra integro-differential equations in one-dimensional bounded and unbounded spatial domains. In a bounded domain, the given parabolic Volterra integro-differential equation is converted to two equivalent equations. Then, a Legendre-collocation method is used to solve them and finally a linear algebraic system is obtained. For the unbounded case, we use the algebraic mapping to transfer the problem on a bounded domain and then apply the same presented approach for the bounded domain. In both cases, some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method.

MSC:

65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
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