fa روش تفاضلات متناهی برای حل معادله انتگرال-دیفرانسیل با مشتقات جزئی جبر alg مقاله مستقل Original Manuscript <span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">در این مقاله یک روش عددی بر مبنای</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> تفاضلات متناهی </span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">برای حل </span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">مسئله انتگرال-دیفرانسیل </span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">با مشتقات جزئی </span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">با هستۀ منفرد</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> ارائه شده است. ابتدا </span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">یک الگورتیم عددی برای حل مسئله براساس طرح کرانک-نیکلسون با شرایط داده شده ارائه و سپس گسسته‌سازی انتگرال منفرد را برای حل این مسئله به‌کار می‌بریم.</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> در ادامه برای نشان دادن کارایی روش بیان شده&nbsp; با</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> مقایسۀ جواب تقریبی و دقیق،</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> با روش بی‌اسپلاین مکعبی</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> نتیجه می‌گیریم که روش ارائه شده از دقت و کارائی لازم برخوردار است.</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> در ادامه شکل تقریبی نیز رسم شده است. سرعت بالای محاسبات، سهولت در به‌دست آمدن و اطمینان از داشتن جواب تقریبی به‌دلیل اثبات پایداری از مزایای این روش است.</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"></span></span> <strong>Introduction</strong><br> In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. One of the best subjects in the numerical analysis is a finite difference method (FDM). We used (FDM) to solve problems in mathematical physics, integral equations, and&nbsp; engineering, such as electromagnetic potential, fluid flow,&nbsp; radiation heats transfer, laminar boundary-layer theory and mass transport, Abel integral equations, and problem of mechanics or physics. Also in some physical problems such as fluid flow and heat transfer problems, the Laplace equations and the Poisson equations are describe by (FDM).&nbsp; In real life most phenomena are modelled by partial differential equations.<span dir="RTL"></span><br> <strong>Material and methods</strong><br> First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results obtained here can be compared with the cubic B-spline method.<br> <strong>Results and discussion</strong><br> In addition, solving some examples demonstrates the validity and applicability of the approached method, so that the results are reported in the tables and their figures are shown. The high speed of the calculations, and the assurance of having an approximate solution are obtain by proving the stability of the method.<br> <strong>Conclusion</strong><br> The following conclusions were drawn from this research. <ul> <li>Coefficients of the approximate function via Crank-Nicholson scheme are found very easily and therefore many calculations are reduced.</li> <li>The numerical results obtained here can be compared with the cubic B-spline method</li> <li>The assurance of having an approximate solution are obtain by proving the stability of the method.<a href="./files/site1/files/61/8.pdf">./files/site1/files/61/8.pdf</a></li> </ul> <br> <strong>&nbsp;</strong><br> &nbsp;  مسئله انتگرال-دیفرانسیل با هسته منفرد, روش تفاضلات متناهی, تحلیل پایداری.‎ رده بندی ریاضی (2010): 65R20, 45K05 Keywords:  Partial integro-differential equation, Singular kernel, Finite difference method, Stability analysis. Mathematics Subject Classification (2010): 65R20, 45K05. 79 88 http://mmr.khu.ac.ir/browse.php?a_code=A-10-115-2&slc_lang=fa&sid=1 Majid Erfanian مجید عرفانیان erfaniyan@uoz.ac.ir 10031947532846003813 10031947532846003813 Yes University of Zabol دانشگاه زابل، دانشکده علوم، گروه ریاضی Hamed Zeidabadi حامد زیدآبادی h.zeidabadi@yahoo.com 10031947532846003814 10031947532846003814 No Sabzevar University of New Technology دانشگاه فناوری های نوین سبزواز