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MATHEMATICAL ENGINEERING TECHNICAL REPORTS Sinc-collocation Methods for Weakly Singular Fredholm Integral Equations of the Second Kind

Tomoaki Okayama, Takayasu Matsuo, Masaaki Sugihara

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Abstract

In this paper we propose new numerical methods for Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equations. Numerical examples show that the methods achieve exponential convergence, and in this sense the methods improve conventional results where only polynomial convergence have been reported so far.

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What this paper is about

In this paper we propose new numerical methods for Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equations. Numerical examples show that the methods achieve exponential convergence, and in this sense the methods improve conventional results where only polynomial convergence have been reported so far.

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Available abstract

In this paper we propose new numerical methods for Fredholm integral equations of the second kind with weakly singular kernels. The methods are developed by means of the Sinc approximation with smoothing transformations, which is an effective technique against the singularities of the equations. Numerical examples show that the methods achieve exponential convergence, and in this sense the methods improve conventional results where only polynomial convergence have been reported so far.

Key concepts: Sinc function, Mathematics, Integral equation, Fredholm integral equation, Collocation method, Convergence (economics), Gravitational singularity, Applied mathematics

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MATHEMATICAL ENGINEERING TECHNICAL REPORTS Sinc-collocation Methods for Weakly Singular Fredholm Integral Equations of the Second Kind — Research Paper | ScholarLens