https://mma.vgtu.lt/index.php/MMA <p>Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis.&nbsp;<a href="https://journals.vilniustech.lt/index.php/MMA/about">More information ...</a></p> Vilnius Gediminas Technical University en-US Mathematical Modelling and Analysis 1392-6292 <p>Authors who publish with this journal agree to the following terms</p> <ul> <li class="show">that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;</li> <li class="show">that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.</li> <li class="show">on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 <a href="https://creativecommons.org/licenses/by/4.0/legalcode">https://creativecommons.org/licenses/by/4.0/legalcode</a>. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.</li> </ul> <p>For authors that are not copyright owners in the work (for example government employees), please <a href="mailto:%20journals@vilniustech.lt">contact VILNIUS TECH</a>to make alternative agreements.</p> https://mma.vgtu.lt/index.php/MMA/article/view/18354 <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> ZhiPeng Liu DongYa Tao Chao Zhang Copyright (c) 2024 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0 2024-05-14 2024-05-14 29 3 387–405 387–405 10.3846/mma.2024.18354 https://mma.vgtu.lt/index.php/MMA/article/view/18535 <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> Haniye Dehestani Yadollah Ordokhani Mohsen Razzaghi Copyright (c) 2024 The Author(s). Published by Vilnius Gediminas Technical University. http://creativecommons.org/licenses/by/4.0 2024-05-14 2024-05-14 29 3 406–425 406–425 10.3846/mma.2024.18535