Name
Abstract | ||
|---|---|---|
We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter ¿ to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of ¿, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s11075-015-0013-7 | Numerical Algorithms |
Keywords | Field | DocType |
Multi-step iterative methods,Multi-step Newton method,Systems of nonlinear equations,Partial differential equations,Discretization methods for partial differential equations | Mathematical optimization,Nonlinear system,Iterative method,Mathematical analysis,Relaxation (iterative method),Numerical partial differential equations,Local convergence,Adomian decomposition method,Mathematics,Multigrid method,Newton's method | Journal |
Volume | Issue | ISSN |
71 | 3 | 1017-1398 |
Citations | PageRank | References |
7 | 0.55 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fayyaz Ahmad | 1 | 49 | 10.88 |
| E. Tohidi | 2 | 52 | 9.65 |
| Juan A. Carrasco | 3 | 116 | 21.24 |