An efficient algorithm for solving Fredholm integral equations using piecewise quadratic interpolation (original) (raw)
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A Computational Approach to the Fredholm Integral Equation of the Second Kind
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The Fredholm integral equation of the second kind is of widespread use in many realms of engineering and applied mathematics. Among the variety of numerical solutions to this equation, the qudrature method and its modification are remarkable. The latter aims at reducing the computational complexity of the quadrature method. In this paper, we present Mathematica programs that utilize the modified quadrature method to solve the equation.
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Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials
Journal of Scientific Research, 2010
In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are used as the approximation of basis functions. Examples are considered to verify the effectiveness of the proposed derivations, and the numerical solutions guarantee the desired accuracy. Keywords: Fredholm integral equation; Galerkin method; Bernstein polynomials. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.4483 J. Sci. Res. 2 (2), 264-272 (2010)