Shahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48593120241201An accurate h-pseudospectral method for numerical solution of the Bratu-type equations11210462510.48308/CMCMA.3.1.1ENHaniehKarampour BeiranvandDepartment of Mathematics, Tafresh University, Tafresh 39518-79611, IranMohammad AliMehrpouyaDepartment of Mathematics, Tafresh University, Tafresh 39518-79611, Iran.Journal Article20240406In this study, an accurate method is developed for solving both initial and boundary value problems of the Bratu-type equations arising in various physical and chemical phenomena. In particular, we investigate the Bratu-Gelfand problem, which is of interest to many researchers because of the behavior of the solution. In the designed methodology, the problem is discretized using a h-pseudospectral method and therefore, solving the problem is reduced to solve a system of nonlinear equations. Numerical results of two examples are presented at the end and the comparison is made with the existing numerical or analytical solvers to show the efficiency and accuracy of the proposed method.https://cmcma.sbu.ac.ir/article_104625_1b67c59c3a19f7535f0af102657b9030.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48593120241201Exponential Gegenbauer collocation method for solving the MHD Falkner-Skan equation132010474510.48308/CMCMA.3.1.13ENFatemehBaharifardSchool of Computer Science, Institute for Research in Fundamental Sciences (IPM)Journal Article20230512In this paper, we aim to introduce a<br />weighted orthogonal system on the half-line based on the<br />exponential Gegenbauer functions. We use these functions in<br />collocation method to solve MHD Falkner-Skan equation, which<br />arises in the study of laminar boundary layers exhibiting<br />similarity on the semi-infinite domain.<br />This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming the domain of the problem to a finite domain. We make a comparison<br />between the results of the proposed system with the numerical<br />results to show that the present method<br />has an acceptable accuracy. https://cmcma.sbu.ac.ir/article_104745_f95f90dae6cb3ba3e41fe1694e16bb1a.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48593120241201Regularization properties of range restricted LSQR method for solving large-scale linear discrete ill-posed problems213710485210.48308/CMCMA.3.1.21ENHuiZhangDepartment of Basic Courses, Jiangsu Police Institute, Nanjing 210031, P.R. ChinaHuaDaiSchool of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. ChinaJournal Article20240812The LSQR iterative method is one of the most popular methods for solving large-scale linear discrete ill-posed problem $Ax=b$ with an error-contaminated right-hand side.<br />In this paper, we consider the regularization properties of range restricted LSQR (RRLSQR) method. The iteration number $k$ always acts as the regularization parameter because of the semi-convergence. In order to verify whether or not the RRLSQR method finds a 2-norm filtering best regularization solution for severely, moderately and mildly ill-posed problems, we present the $sin \Theta$ theorems for the 2-norm distances between the $k$ dimensional left and right Krylov subspaces generated by Lanczos bidiagonalization and the $k$ dimensional dominant left and right singular subspaces of $A$, and estimate the distances for the three kinds problems assuming that the singular values are simple, and develop a regularized RRLSQR method for solving linear discrete ill-posed problems. Numerical experiments confirm our theoretical results and show the efficiency of the proposed method. https://cmcma.sbu.ac.ir/article_104852_2605b7beea2e5b6f4102be51a2714a66.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48593120241201A fully discretization approach for nonlinear Phi-four equations384510490110.48308/CMCMA.3.1.38ENMohammad AliMehrpouyaDepartment of Mathematics, Tafresh University, Tafresh 39518-79611, Iran.Journal Article20240802In this paper, a fully discretization approach is established for accurate and efficient solution of nonlinear time-dependent Phi-four equations arising in particle physics and quantum mechanics. In the suggested approach, the lobatto pseudospectral method is used to discretize the desired problem. So, the Phi-four equation is converted into a set of nonlinear algebraic equations. The primary benefit of the suggested approach is that, it produces excellent results with just few discretization points and has a fast rate of convergence. Numerical results are showcased to verify the precision and effectiveness of the suggested approach for solving nonlinear Phi-four equations.https://cmcma.sbu.ac.ir/article_104901_614d62fa90b8e1549ad38d905ee4818f.pdf