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Abstract

In this research, the two-dimensional parabolic integral-differential equation was solved using one of the numerical methods, which is the finite element method (Galerkin) on triangular elements. This method was chosen to make extensive use of finite elements because it has many high-quality numerical properties. The main benefit of finite elements is their ability to solve a wide range of problems in different computational fields in different forms, especially complex ones that cannot be solved by other numerical methods. Given the semi-discrete error estimates for the normal space H1, the polynomial linear boundary element space defined in triangles was used to describe space and the inverse Euler method was used to describe time. The discriminant rules used to differentiate the Volterra integral term are also chosen to be compatible with time phase diagrams. In addition, the numerical solutions of the two-dimensional differential integral equation of the equivalent type are compared with the exact solutions, and finally the final results of the solutions are displayed graphically using MATLAB. Finite element Galerkin error analysis was taken into account when using a mesh of triangular elements on the differential equation in two-dimensional space.

Keywords

Backward-Euler, Parabolic Integro-Differential, Quadrature procedures, Two-dimensional, Volterra integral term

Subject Area

Mathematics

Article Type

Article

First Page

979

Last Page

987

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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