Computational Methods for Integral Equations
Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides a readable account of techniques for their numerical solution. The authors devote their attention primarily to efficient techniques using high order approximations, taking particular account of situations where singularities are present. The classes of problems which arise frequently in practice, Fredholm of the first and second kind and eigenvalue problems, are dealt with in depth. Volterra equations, although attractive to treat theoretically, arise less often in practical problems and so have been given less emphasis. Some knowledge of numerical methods and linear algebra is assumed, but the book includes introductory sections on numerical quadrature and function space concepts. This book should serve as a valuable text for final year undergraduate or postgraduate courses, and as an introduction or reference work for practising computational mathematicians, scientists and engineers.
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The space if 2ab
Introduction to the theory of linear integral equa
The Nystrom quadrature method for Fredholm
Quadrature methods for Volterra equations of
Eigenvalue problems and the Fredholm
Expansion methods for Fredholm equations of
Analysis of the Galerkin method with orthogonal
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accuracy algorithm bound Chapter characteristic value Chebyshev expansion Chebyshev polynomials choice coefficients computed consider derivatives discussion driving term eigenfunction eigenvalues equation x(s error estimate evaluate exact solution example exists expansion method FE2SR FFTNA Fredholm equations Galerkin equations Galerkin method Gauss rule Gauss-Chebyshev Gauss-Legendre rule given hence Hermitian if2 functions integral equation integrand integro-differential equations interval iterative scheme least squares linear low-order matrix N-point Neumann series Newton-Cotes rule nonlinear norm numerical quadrature numerical solution Nystrom equations Nystrom method obtain operator ordinary differential equations orthogonal orthonormal parameters PMODNA problem families procedure product integration quadrature errors quadrature points quadrature rule rapid convergence regular value repeated Trapezoid Runge-Kutta method satisfies second kind Section sequence Simpson's rule singular singular functions smooth solution x(s solve steplength Table techniques Theorem Trapezoid rule truncated vector Volterra equations weight function weight function w(s yields zero