نوع مقاله : مقاله پژوهشی
نویسنده
گروه ریاضی، دانشگاه سراوان، سراوان، ایران
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسنده [English]
Since most integral equations of the first kind are ill-posed, in this article we tried to present a method based on Legendre wavelets to solve some of them. The proposed method is that at first all the components of the equation are expressed in matrix form based on Legendre wavelet functions, then these matrices are replaced in the main equation. This method, along with the collocation method, adjusts the equation to a system of algebraic equations, which can be solved by usual numerical or analytical methods. To show the convergence of the method, some computable error bounds are obtained by preparing some theorems and lemmas. Moreover, the stability analysis, the existence, and uniqueness of the solution are investigated. Numerical results with comparisons are given to confirm the reliability of the proposed method. In practice, in order to check the stability, we calculated the condition number in the examples, and also the convergence rate was calculated and the convergence was displayed in graphs by the ratio test. The outcomes reveal that this method is very effective and more accurate than those of the literature. Also, in many cases, one can get the exact solution to the problem.
کلیدواژهها [English]
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