https://mma.vgtu.lt/index.php/MMA/issue/feedMathematical Modelling and Analysis2024-05-14T18:25:42+03:00Prof. Dr Raimondas Čiegismma@vilniustech.ltOpen Journal Systems<p>Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis. <a href="https://journals.vilniustech.lt/index.php/MMA/about">More information ...</a></p>https://mma.vgtu.lt/index.php/MMA/article/view/18354An efficient spectral method for nonlinear Volterra integro-differential equations with weakly singular kernels2024-05-14T18:25:42+03:00ZhiPeng Liuliuzhipeng9707@163.comDongYa Taodongyatao@jsnu.edu.cnChao Zhangzcxz1977@163.com<p>For Volterra integro-differential equations (VIDEs) with weakly singular kernels, their solutions are singular at the initial time. This property brings a great challenge to traditional numerical methods. Here, we investigate the numerical approximation for the solution of the nonlinear model with weakly singular kernels. Due to its characteristic, we split the interval and focus on the first one to save operation. We employ the corresponding singular functions as basis functions in the first interval to simulate its singular behavior, and take the Legendre polynomials as basis functions in the other one. Then the corresponding hp-version spectral method is proposed, the existence and uniqueness of solution to the numerical scheme are proved, the hp-version optimal convergence is derived. Numerical experiments verify the effectiveness of the proposed method.</p>2024-05-14T13:54:51+03:00Copyright (c) 2024 The Author(s). Published by Vilnius Gediminas Technical University.https://mma.vgtu.lt/index.php/MMA/article/view/18535An accurate numerical scheme for three-dimensional variable-order time-fractional partial differential equations in two types of space domains2024-05-14T18:25:42+03:00Haniye Dehestanih.dehestani@alzahra.ac.irYadollah Ordokhaniordokhani@alzahra.ac.irMohsen Razzaghirazzaghi@math.msstate.edu<p>We consider the discretization method for solving three-dimensional variable-order (3D-VO) time-fractional partial differential equations. The proposed method is developed based on discrete shifted Hahn polynomials (DSHPs) and their operational matrices. In the process of method implementation, the modified operational matrix (MOM) and complement vector (CV) of integration and pseudooperational matrix (POM) of VO fractional derivative plays an important role in the accuracy of the method. Further, we discuss the error of the approximate solution. At last, the methodology is validated by well test examples in two types of space domains. In order to evaluate the accuracy and applicability of the approach, the results are compared with other methods.</p>2024-05-14T14:16:42+03:00Copyright (c) 2024 The Author(s). Published by Vilnius Gediminas Technical University.