A Comparison of Two Projection Methods in Solving System of Fredholm and Volterra Integral Equations

Monireh Nosrati Sahlan

Abstract


In this paper, linear B-spline wavelets are applied for the efficient solution of system of Fredholm and Volterra linear integral equations of the second kind. Collocation and galerkin methods are utilized and wavelets are employed as test and weight
functions. The performance of these methods is compared on the integral equations. On the other hand Because of some significant properties of these wavelets, such semi orthogonality, having vanishing moments are compact support, the operational matrices are so sparse, in fact there is a considerable difference between the absolute value of largest and smallest entire of matrices. Thus an
appropriate thresholding parameter can be chosen for reduction the relevant matrices. Consequently the propounded methods have a major advantage in economy of memory requirement and operational time. Accuracy and application of the introduced method are demonstrated through illustrative examples and results are shown in tables.

Keywords


system of integral equations; linear B-spline wavelets; Fredholm and Volterra integral equations; collocation method; Galerkin method

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