Spline Function Approximations for Solutions of Ordinary Differential Equations
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Publication:5558195
DOI10.1137/0704038zbMath0171.36301OpenAlexW1977449329MaRDI QIDQ5558195
T. D. Talbot, Frank R. Loscalzo
Publication date: 1967
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/euclid.bams/1183528860
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𝑂(ℎ^{2𝑛+2-𝑙}) bounds on some spline interpolation errors ⋮ A deficient spline function approximation to fourth-order differential equations ⋮ On quadratic spline interpolation ⋮ Initial value problems with retarded argument solved by iterated quadratic splines ⋮ \(2h\)-step spline method for the solution of delay differential equations ⋮ On some 4-Point Spline Collocation Methods for Solving Ordinary Initial Value Problems ⋮ Quadratic spline ⋮ Numerical solutions of second-order matrix models using cubic-matrix splines ⋮ On the relations between B\(_2\)VMs and Runge-Kutta collocation methods ⋮ On the application of spline functions to initial value problems with retarded argument ⋮ Lösung von gewöhnlichen Differentialgleichungen mit nichtlinearen Splines ⋮ Numerical approximations of second-order matrix differential equations using higher degree splines ⋮ A suboptimal control algorithm for constrained problems using cubic splines ⋮ Approximating and computing nonlinear matrix differential models ⋮ Splineapproximationen von beliebigem Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil II ⋮ Numerische Lösung gewöhnlicher Differentialgleichungen mit Splinefunktionen ⋮ Spline function approximation for differential equations ⋮ Application of spline functions to neutral delay-differential equations ⋮ A numerical method for solving stochastic optimal control problems with linear control ⋮ Numerical solution of Volterra integral equations by spline functions ⋮ Quadrature formulas descending from BS Hermite spline quasi-interpolation ⋮ Convergence rates of Gaussian ODE filters ⋮ Linear dependence relations for polynomial splines at midknots ⋮ Conservative spline methods for second-order IVPs of ODEs ⋮ Gradient superconvergence for a class of semi-cardinal interpolation schemes with cubic and quintic B-splines ⋮ Approximate Numerical Solutions of Autonomous Second-Order Matrix Models Using Cubic Matrix Splines ⋮ Numerical solutions of matrix differential models using cubic matrix splines. II ⋮ Convergence of spline collocation for Volterra integral equations ⋮ The numerical solution of nonlinear differential equations by spline functions ⋮ Numerical solutions of matrix differential models using higher-order matrix splines ⋮ One-Step Piecewise Polynomial Galerkin Methods for Initial Value Problems ⋮ A survey on parametric spline function approximation ⋮ Spline Approximation to the Solution of the Volterra Integral Equation of the Second Kind ⋮ Stability of spline approximation and the restoration of grid functions ⋮ Spline techniques for solving first-order evolution equations in Banach spaces ⋮ Asymptotically efficient parameter estimation for ordinary differential equations ⋮ A new method to solve numeric solution of nonlinear dynamic system ⋮ Stability of 2h-step spline method for delay differential equations ⋮ Splineapproximationen von beliebigem Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil I ⋮ THEORETICAL AND NUMERICAL STUDIES OF TWO POINT BOUNDARY VALUE PROBLEMS USING TRIGONOMETRIC AND EXPONENTIAL CUBIC B-SPLINES ⋮ NUMERICAL TREATMENT OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS USING DIFFERENT CUBIC B-SPLINE FUNCTIONS ⋮ L-splines ⋮ On piecewise polynomial interpolation in rectangular polygons ⋮ A Galerkin approximation for the initial-value problem for linear second- order differential equations ⋮ Piecewise polynomial Taylor methods for initial value problems ⋮ Spline-Funktionen bei der Lösung von Integralgleichungen. (Spline functions for solving integral equations.) ⋮ A one-step integration routine for normal differential systems, based on Gauss-Legendre quadrature ⋮ Bicubic spline interpolation in L-shaped domains ⋮ On the divergence of collocation solutions in smooth piecewise polynomial spaces for Volterra integral equations ⋮ A probabilistic model for the numerical solution of initial value problems ⋮ Numerical solution of stiff and convection-diffusion equations using adaptive spline function approximation ⋮ A deficient spline function approximation to systems of first-order differential equations. II ⋮ Numerical method for the solution of linear boundary-value problems for integrodifferential equations based on spline approximations ⋮ One-Step Piecewise Polynomial Multiple Collocation Methods for Initial Value Problems ⋮ A finite element approximation for the initial-value problem for nonlinear second-order differential equations ⋮ Numerical solution of matrix differential models using cubic matrix splines
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