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The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(1):101-116; doi:10.1093/qjmam/29.1.101
© 1976 by Oxford University Press
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CONVERGENCE OF A PROJECTION METHOD FOR FOURIER-TRANSFORMED INTEGRAL EQUATIONS

F. PREMUDA and T. TROMBETTI

( Comitato Nazionale per l'Energia Nucleare Centro di Calcolo, Bologna, Italy )

A unified formulation of some recently proposed Fourier-transform methods is given here for linear integral equations over a finite interval with displacement kernels. The convergence of a sequence of approximate solutions to the exact solution is established in the framework of a projection method. Under certain conditions the existence of monotonically convergent sequences of approximate eigenvalues is proved. The properties of the matrix equations which are equivalent to the projected integral equations are discussed with reference to a typical physical case, in order to estimate the approximation error and explain the rapidity of convergence numerically ascertained by various authors.


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