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- W116336744 abstract "This chapter discusses Runge–Kutta (R–K) processes. The R–K scheme is basically a substitution method of the form y n+1 = y n + h n Ф RK (x n , y n ; h) with the increment function Ф RK given as a weighted mean of the slopes at specific points. A different method was proposed to avoid the need to solve large sets of nonlinear equations with IRK and semi-implicit R–K methods. The chapter describes Rosenbrock method that involved the class of s -stage numerical integrators for autonomous differential systems. The main advantage of the Rosenbrock method is the considerable reduction in the linear algebra normally associated with the implicit and semi-implicit R–K methods at the cost of at least one evaluation of the Jacobian at every integration step. The main attraction of implicit R–K methods is their strong stability properties. However, all such methods require the solution of systems of nonlinear equations that define the internal slopes. If the R–K process is semi-implicit, then the coupled, simultaneous nonlinear system splits into s uncoupled nonlinear systems. Rosenbrock methods further reduce the problem to s uncoupled linear systems." @default.
- W116336744 created "2016-06-24" @default.
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- W116336744 date "1988-01-01" @default.
- W116336744 modified "2023-09-26" @default.
- W116336744 title "RUNGE-KUTTA PROCESSES" @default.
- W116336744 doi "https://doi.org/10.1016/b978-0-12-249930-2.50008-4" @default.
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