A Steffensen’s type method in Banach spaces with applications on boundary-value problems. (English) Zbl 1139.65040
Summary: A modified Steffensen’s type iterative scheme for the numerical solution of a system of nonlinear equations is studied. Two convergence theorems are presented. The numerical solution of boundary-value problems by the multiple shooting method using the proposed iterative scheme is analyzed.
MSC:
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 47J25 | Iterative procedures involving nonlinear operators |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
Keywords:
Steffensen’s scheme; shooting method; boundary-value problems; numerical examples; system of nonlinear equations; convergenceReferences:
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