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An easily implementable fourth-order method for the time integration of wave problems. (English) Zbl 0761.65074
The authors construct a 4th-order three stage difference scheme for ordinary differential equations by composing three implicit second order midpoint schemes. This method can also be applied to partial differential equations.
The constructed scheme is not \(A\)-stable as the authors point out. However its instability region is just a very little “circle” about - 1.18 on the real axis. Detailed results can be found in the paper [Comput. Math. Appl. 25, 35-44 (1993)].

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L05 Numerical methods for initial value problems
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65L20 Stability and convergence of numerical methods for ordinary differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
34L05 General spectral theory of ordinary differential operators
35L60 First-order nonlinear hyperbolic equations
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