Título:
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Multi-step frozen Jacobian iterative scheme for solving IVPs and BVPs based on higher order Fréchet derivatives
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Autor/a:
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Ilyas, Iqra; Ali, Zulqar; Ahmad, Fayyaz; Ullah, Malik Zaka; Alshomrani, Ali Saleh
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Otros autores:
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Universitat Politècnica de Catalunya. GAA - Grup d'Astronomia i Astrofísica |
Abstract:
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A multi-step frozen Jacobian iterative scheme for solving system of nonlinear equations associated with IVPs (initial value problems) and BVPs (boundary value problems) is constructed. The multi-step iterative schemes consist of two parts, namely base method and a multi-step part. The proposed iterative scheme uses higher order Fr ´echet derivatives in the base method part and offers high convergence order (CO) 3s + 1, here s is the number of steps.
The increment in the CO per step is three, and we solve three upper and lower triangles systems per step in the multi-step part. A single inversion of the is not working in latexfrozen Jacobian is required and in fact, we avoid the direct inversion of the frozen Jacobian by computing the LU factors. The LU-factors are utilized in the multi-step part to solve upper and lower triangular systems repeatedly that makes the iterative scheme computationally efficient. We solve a set of IVPs and BVPs to show the validity, accuracy and efficiency of our proposed iterative scheme. |
Abstract:
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Peer Reviewed |
Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals -Differential equations, Partial -Multi-step iterative schemes -Systems of nonlinear equations -Frozen
Jacobian -Initial and boundary value problems -Higher order Fréchet derivatives. -Equacions diferencials parcials -35G30 -35G31 -34L30 -65H20 |
Derechos:
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Tipo de documento:
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Artículo - Versión publicada Artículo |
Editor:
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Punjab University
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