A highly accurate scheme for solving the thin plate equation

A. Tazdayte ^[1] ; H. Allouche ^[1] ; K. Tigma ^[1]
1. [1] Faculty of Sciences, Department of Mathematics and Computer Sciences MAN-TA Team, Moulay Ismail University, Meknes, Morocco
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 2, 2024, págs. 291-305
Idioma: inglés
DOI: 10.1007/s40324-023-00324-6
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Resumen
- This paper reports a new bi-quintic B-spline collocation method for numerically solving biharmonic problems with Dirichlet boundary conditions on the rectangular domain. Solving these problems with standard bi-quintic B-spline collocation provides only second-order convergence. To overcome this limitation, we formulate a sixth-order collocation scheme, namely, the one-step left and right-hand sides perturbation collocationmethod. Themain idea consists of applying a high-order perturbation on the residual operator, which will annihilate the derivatives of orders greater than 4, increasing the convergence rate. Convergence analysis is discussed and numerical illustrations are presented to confirm the efficiency of the proposed method.