Piecewise Polynomial Collocation for Volterra-type Integral Equations of the Second Kind |
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Authors: | BRUNNER, H. EVANS, M. D. |
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Affiliation: | Department of Mathematics, Dalhousie University Halifax B3H 4H8, Nova Scotia, Canada Munich International School, Schloss Buchhof 8136 Percha bei Starnberg, Germany |
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Abstract: | The exact solution of a given integral equation of the secondkind of Volterra type(with regular or weakly singular kernel)is projected into the space of (continuous) piecewise polynomialsof degree m 1 and with prescribed knots by using collocationtechniques. It is shown that a number of discrete methods forthe numerical solution of such equations based on product integrationtechniques or on finite-difference methods are particular discreteversions of collocation methods of the above type. The errorbehaviour of approximate solutions obtained by collocation (includingtheir discretizations) is discussed. |
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