Abstract
To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.
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Communicated by YE Zhi-ming
Project supported by the National Natural Science Foundation of China (No.10271074)
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Gu, Cq., Pan, Bz. & Wu, Bb. Orthogonal polynomials and determinant formulas of function-valued Padé-type approximation using for solution of integral equations. Appl Math Mech 27, 853–860 (2006). https://doi.org/10.1007/s10483-006-0616-y
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DOI: https://doi.org/10.1007/s10483-006-0616-y
Key words
- generalized linear functional
- function-valued
- Padé-type approximation
- Fredholm integral equation
- orthogonal polynomial
- determinant formula