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• W858359518 abstract "Recent surveys have revealed that the majority of numericalmethods for the solution of integral equations use one of twomain techniques for generating a set of simultaneousequations for their solution. Either the unknown function isexpanded as a combination of basis set functions and theresulting coefficients found, or the integral is discretizedusing quadrature formulae. The latter results in simultaneousequations for the solution at the quadrature abscissae.The thesis proposes techniques based on various direct iterativemethods, including refinements of residual correction whichhold no restrictions for nonlinear integral equations. Newimplementations of successive approximations and Newton'smethod appear. The latter compares particularly well with otherversions as the evaluation of the Jacobian can be madeequivalent to the solution of matrix equations of relativelysmall dimensions. The method can be adapted to the solution offirst-kind equations and has been applied to systems of integralequations. The schemes are designed to be adaptive with the aidof the progressive quadrature rules of Patterson or Clenshaw andCurtis and interpolation formulae. The Clenshaw-Curtis rule isparticularly favoured as it delivers error estimates.A very powerful routine for the solution of a wide range of integral equations has resulted with the inclusion of a newefficient method for calculating singular integrals.Some work is devoted to the conversion of differential tointegral or integro-differential equations and comparing themerits of solving a problem in its original and converted forms.Many equations are solved as test examples throughout the thesisof which several are of physical significance. They includeintegral equations for the slowing down of neutrons, theLane-Emden equation, an equation arising from a chemical reactorproblem, Chandrasekhar's isotropic scatter ing of radiationequation and the Blasius equation in boundary layer theory." @default.
• W858359518 created "2016-06-24" @default.
• W858359518 creator A5020395649 @default.
• W858359518 date "1984-01-01" @default.
• W858359518 modified "2023-09-27" @default.
• W858359518 title "Development of numerical methods for the solution of integral equations" @default.
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• W858359518 hasPublicationYear "1984" @default.
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