New Stable Numerical Solutions of Singular Integral Equations of Abel Type by Using Normalized Bernstein Polynomials
نویسندگان
چکیده
A new numerical method, based on the normalized Bernstein polynomials for solving singular integral equations of Abel type is presented here in this paper. We construct an othonormal family { } i n i b 0 = of polynomials of degree n from the th n degree Bernstein polynomials n i B and use them as a basis to approximate the known and unknown functions ) (x f and ) (x φ respectively in the Abel’s integral equations. Then orthogonality is used to reduce the integral equation to a system of algebraic equations which can be solved easily. The method is quite accurate and stable even when the approximations are performed by orthonormal Bernstein polynomials n i b of degree as low as 5 , as illustrated by the given numerical examples with varying degree of noise terms ε added to ) (x f . Mathematics Subject Classification: 45E10; 45D05
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