Abstract
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.
Iqra Ilyas, Zulfiqar Ali, Fayyaz Ahmad, Malik Zaka Ullah, Ali Saleh Alshomrani. (2017) Multi-step frozen Jacobian iterative scheme for solving IVPs and BVPs based on higher order Fr´echet derivatives, Punjab University Journal of Mathematics, Volume 49, Issue 1.
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