Name
Title | ||
|---|---|---|
A stopping criterion for the Newton-Raphson method in implicit multistep integration algorithms for nonlinear systems of ordinary differential equations |
Abstract | ||
|---|---|---|
In the numerical solution of ordinary differential equations, certain implicit linear multistep formulas, i.e. formulas of type ∑kj=0 &agr;jxn+j - h ∑kj=0 &bgr;jxn+j = 0, (1) with &bgr;k ≠ 0, have long been favored because they exhibit strong (fixed-h) stability. Lately, it has been observed [1-3] that some special methods of this type are unconditionally fixed-h stable with respect to the step size. This property is of great importance for the efficient solution of stiff [4] systems of differential equations, i.e. systems with widely separated time constants. Such special methods make it possible to integrate stiff systems using a step size which is large relative to the rate of change of the fast-varying components of the solution. |
Year | DOI | Venue |
|---|---|---|
1971 | 10.1145/362663.362745 | Commun. ACM |
Keywords | Field | DocType |
linear multistep formulas,efficient solution,differential equation,stiff system,fast-varying component,fixed-h stable,implicit multistep integration algorithm,newton-raphson method,ordinary differential equations,step size,stopping criterion,special method,nonlinear system,certain implicit linear multistep,ordinary differential equation,numerical solution,newton raphson method,rate of change,time constant | Runge–Kutta methods,Linear multistep method,Numerical methods for ordinary differential equations,Explicit and implicit methods,Exponential integrator,Mathematical analysis,Backward differentiation formula,Collocation method,Mathematics,Numerical stability | Journal |
Volume | Issue | ISSN |
14 | 9 | 0001-0782 |
Citations | PageRank | References |
1 | 0.37 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| W. Liniger | 1 | 25 | 28.27 |