هدف اصلی این تحقیق یافتن جواب تحلیلی رده ای از معادلات انتگرال فوق منفرد نوع دوم به نام پراندتل است که در مباحث فنی من جمله مکانیک پدید می آید. بدین منظور از یک روش بهبود یافته‌ی جدید و سریع بر اساس روش اختلال هموتوپی استفاده می شود. با ارائه‌ی مثال‌هایی نشان خواهیم داد که روش اختلال هموتوپی استاندارد در حالت کلی برای حل این رده از معادلات انتگرال همگرا نبوده و روش اختلال هموتوپی اصلاح شده نیز صرفاً زمانی همگرا است که جواب دقیق معادله از قبل مشخص باشد، اما روش پیشنهادی در این مقاله، بدون نیاز به دانستنن جواب دقیق مسئله، جواب دقیق این رده از معادلات انتگرال را در دومین تکرار از روش مشخص می‌کند. نتایج حاصل از مثالها مزایای روش بهبود یافته اختلال هموتوپی جدید را در مقایسه با روشهای استاندارد و اصلاح شده اختلال هموتوپی از جمله سادگی و سرعت بیشتر را نشان می دهد. Manuscript profile

In this study, a new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second kind fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the fuzzy integral equation is converted to a system of crisp integral equations. Then, this system is solved by using the reproducing kernel method free of the Gram-Schmidt orthogonalization process. Also, two numerical algorithms are proposed based on applying the Gram-Schmidt process and without using it. The general form of numerical solution accordingly the reproducing kernel method is introduced and the convergence theorem of solution of the proposed scheme to the exact solution is proved. Finally, a sample fuzzy integral equation is solved by means of both suggested algorithms and the results are compared for differents points and levels. Due to the difficulties in applying the Gram-Schmidt process, the obtained results of the new algorithm are satisfactory. Manuscript profile

Burgers' equation arises in various areas of applied mathematics,‎‎such as modeling of dynamics‎, ‎heat conduction‎, ‎and acoustic‎‎waves‎ Also‎, ‎this equation has a large variety of applications in‎‎the modeling of water in unsaturated soil‎, ‎dynamics of soil‎‎water‎, ‎models of traffic‎, ‎turbulence and fluid flow‎, ‎mixing and‎‎turbulent diffusion. Many researchers tried to find analytic and numerical solutions of‎‎ this equation by different methods.Sinc method is a powerful numerical tool for finding fast and‎‎accurate solution in various areas of problems.‎In this paper‎, ‎numerical solution of Burgers' equation‎‎is considered by applying Sinc method‎. ‎For this purpose‎, ‎we apply‎‎Sinc method in cooperative with a classic finite difference‎‎formula to‎ ‎Burgers'equation‎. ‎‎The purpose of this paper is to extend the application of the‎‎sinc method for solving Burgers'equation by considering stability‎‎analysis of the method.‎ Numerical examples are provided to verify the validity of proposed method Manuscript profile

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1for both cases b2-4ac L 0and b2-4ac G 0. Manuscript profile