Two-step fourth order P-stable methods for second order differential equations
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Publication:5904710
DOI10.1007/BF01933163zbMath0457.65053OpenAlexW2321316423MaRDI QIDQ5904710
Publication date: 1981
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01933163
Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)
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Families of two-step fourth order \(P\)-stable methods for second order differential equations ⋮ On ninth order, explicit Numerov-type methods with constant coefficients ⋮ Efficient fourth order P-stable formulae ⋮ Block generalized Störmer-Cowell methods applied to second order nonlinear delay differential equations ⋮ A class of Rosenbrock-type schemes for second-order nonlinear systems of ordinary differential equations ⋮ Unconditionally stable methods for second-order Fredholm integro-differential equations ⋮ Two-step hybrid methods for periodic initial value problems ⋮ Variable-order, variable-step methods for second-order initial-value problems ⋮ \(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations ⋮ A modified numerov integration method for second order periodic initial-value problems ⋮ Attainable order of theP-stable family of certain two-step methods for periodic second order initial value problems ⋮ PGSCM: A family of \(P\)-stable boundary value methods for second-order initial value problems ⋮ EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs ⋮ AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION ⋮ P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations ⋮ Two-step fourth order P-stable methods for second order differential equations ⋮ An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems ⋮ Stage reduction on P-stable Numerov type methods of eighth order ⋮ Modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ A new kind of high-efficient and high-accurate P-stable Obrechkoff three-step method for periodic initial-value problems ⋮ Hybrid Numerov-type methods with coefficients trained to perform better on classical orbits ⋮ Exponentially-fitted Obrechkoff methods for second-order differential equations ⋮ A class of p-stable linear multistep numerical methods ⋮ A continuous implicit nyström method for solving ordinary second order initial value problems ⋮ NUMEROV-TYPE METHODS FOR OSCILLATORY LINEAR INITIAL VALUE PROBLEMS ⋮ A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS ⋮ EXPLICIT EIGHTH ORDER TWO-STEP METHODS WITH NINE STAGES FOR INTEGRATING OSCILLATORY PROBLEMS ⋮ Two sided error bounds for discretisation methods in special qth order ordinary differential equations ⋮ Efficient P-stable methods for periodic initial value problems ⋮ A quartic \(C^ 3\)-spline collocation method for solving second-order initial value problems ⋮ High accuracy hybrid formula for \(y= f(x,y)\) ⋮ A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y=f(x,y)\) ⋮ Phase properties of high order, almost P-stable formulae ⋮ Analysis of a class of multi-stage, multistep Runge-Kutta methods
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