A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y''=f(x,y)\). (English) Zbl 0934.65079

The authors define the exponential-fitting version of the fourth-order two-step method introduced by M. M. Chawla [BIT 21, 190-193 (1981; Zbl 0457.65053)]. By introducing the concept of ‘ ‘ conditional \(P\)-stability’ ’ of a family of exponential-fitting methods and the parameter \( \theta_{max} \) associated to a conditioned \(P\)-stable family they prove that the new version of Chawla algorithm is conditionally \(P\)-stable with \( \theta_{\max} = 3.4 \). Moreover, a numerical test is reported in order to make out the following two points: the new method with \( \theta < 3.4 \) can be effectively applied to solving stiff problems; due to the exponential-fitting feature, on problems with oscillating solution the method produces more accurate results than its polynomial-fitting companion.
Reviewer: R.Fazio(Messina)


65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems


Zbl 0457.65053


Full Text: DOI


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