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In this paper, an approximate solution for solving weakly singular kernel partial integro-differential equations with time fractional order is proposed. The method is based on using a second-order time difference… Click to show full abstract
In this paper, an approximate solution for solving weakly singular kernel partial integro-differential equations with time fractional order is proposed. The method is based on using a second-order time difference approximation followed by applying the fractional integral operator and piecewise linear interpolation to compute the singularity of the kernel that appear in the discretization process. The stability of the method is also considered in the sense of von Neumann analysis. Numerical examples are solved to demonstrate the validity and applicability of the presented technique.
Journal Title: Asian-european Journal of Mathematics
Year Published: 2017
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