Computational Mathematics

2006, No. 9

I.A. Blatov, E.A. Alasheeva

THE WAVELET-GALERKIN METHOD FOR A FREDGOLM INTEGRAL EQUATION IN TWO-DIMENSIONAL DOMAINS

Mathematical modelling of electrodynamic problems leads to necessity of a integral equations solution with unknown function of two variables. The discreatization of such equations by the standard numerical methods gives systems of simple equations with dense matrix of unacceptable large order. In the paper an approach of spline wavelet usage is proposed. It is shown that majority of matrix elements of systems of simple equations is very small on an absolute value, i.e. matrix is pseudo-air-break. This property allows to approximate it by an air-break matrix and, applying air-break process technique, considerably speed up process of evaluations and to lower the requirements to a random access memory of a computer.