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2020•Journal of Applied Mathematics and PhysicsOpen access

Numerical Simulation for Fredholm Integral Equation of the Second Kind

Peng Guo

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Abstract

This work mainly focuses on the numerical simulation of the Fredholm integral equation of the second kind. Applying the idea of Gauss-Lobatto quadrature formula, a numerical method is developed. For the integral item, we give an approximation with high precision. The existence condition of the solution for the Fredholm equation is given. Furthermore, the error analyses are presented. Finally, the numerical examples verify the theoretical analysis, and show the efficiency of the algorithm we discussed.

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What this paper is about

This work mainly focuses on the numerical simulation of the Fredholm integral equation of the second kind. Applying the idea of Gauss-Lobatto quadrature formula, a numerical method is developed. For the integral item, we give an approximation with high precision. The existence condition of the solution for the Fredholm equation is given. Furthermore, the error analyses are presented. Finally, the numerical examples verify the theoretical analysis, and show the efficiency of the algorithm we discussed.

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Available abstract

This work mainly focuses on the numerical simulation of the Fredholm integral equation of the second kind. Applying the idea of Gauss-Lobatto quadrature formula, a numerical method is developed. For the integral item, we give an approximation with high precision. The existence condition of the solution for the Fredholm equation is given. Furthermore, the error analyses are presented. Finally, the numerical examples verify the theoretical analysis, and show the efficiency of the algorithm we discussed.

Key concepts: Fredholm integral equation, Nyström method, Fredholm theory, Integral equation, Quadrature (astronomy), Mathematics, Gauss, Work (physics)

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