A variant of Steffensen’s method of fourth-order convergence and its applications. (English) Zbl 1208.65064
A variant of Steffensen’s method is presented, which uses divided differences instead of derivatives. Fourth-order convergence is proved. Numerical tests are given for nonlinear algebraic and ordinary differential equations.
Reviewer: János Karátson (Budapest)
MSC:
| 65H05 | Numerical computation of solutions to single equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
Keywords:
nonlinear equations; Newton’s method; Steffensen’s method; derivative free; fourth-order convergence; numerical examplesReferences:
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