Approximate Solution of Nonlinear Differential Equations with the Help of Rational Spline Functions

A method for constructing an approximate solution in the form of a rational spline function is proposed for initial value problems in the case of first- and second-order differential equations solvable for the highest derivative. A spline function of this type is constructed via the transition to a...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2021-08, Vol.61 (8), p.1252-1259
Main Authors: Magomedova, V. G., Ramazanov, A.-R. K.
Format: Article
Language:English
Subjects:
Approximation
Boundary value problems
Computational Mathematics and Numerical Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Nonlinear equations
Ordinary Differential Equations
Spline functions
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Summary:A method for constructing an approximate solution in the form of a rational spline function is proposed for initial value problems in the case of first- and second-order differential equations solvable for the highest derivative. A spline function of this type is constructed via the transition to a system of scalar equations that is reduced to solving at most one nonlinear equation with one unknown and to making sequential substitutions of previously determined values.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542521080042