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

被引：0

作者：

Magomedova, V. G. ^{[1
]}

Ramazanov, A-R K. ^{[1
,2
]}

机构：

[1] Dagestan State Univ, Makhachkala 367000, Dagestan, Russia

[2] Russian Acad Sci, Dagestan Sci Ctr, Makhachkala 367032, Dagestan, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2021年 / 61卷 / 08期

关键词：

rational spline functions; interpolation spline functions; approximate solution of differential equations;

D O I：

10.1134/S0965542521080042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1252 / 1259

页数：8

共 50 条

[31] APPROXIMATE SOLUTION TO NONLINEAR EQUATIONS OF EVOLUTION
GROGER, K
MATHEMATISCHE NACHRICHTEN, 1971, 49 (1-6) : 375 - &
[32] On approximate solution of nonlinear operator equations
V. P. Tanana
Siberian Mathematical Journal, 1998, 39 : 1017 - 1025
[33] The approximate solution of nonlinear operational equations
Takaci, D
Takaci, A
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2004, 65 (1-2): : 65 - 79
[34] On approximate solution of nonlinear operator equations
Tanana, VP
SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (05) : 1017 - 1025
[35] On the solution of differential equations with fuzzy spline wavelets
Shmilovici, A
Maimon, O
FUZZY SETS AND SYSTEMS, 1998, 96 (01) : 77 - 99
[36] SPLINE FUNCTIONS AND CAUCHY PROBLEMS .2. APPROXIMATE SOLUTION OF DIFFERENTIAL-EQUATION Y''=F(X,Y,Y') WITH SPLINE FUNCTIONS
FAWZY, T
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1977, 29 (3-4): : 259 - 271
[37] APPROXIMATION BY RATIONAL FUNCTIONS, SOLUTION OF THE EQUATIONS
Cherednichenko, V. G.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2010, 7 : C283 - C289
[38] The numerical solution of first order delay integro-differential equations by spline functions
Ayad, A
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2001, 77 (01) : 125 - 134
[39] The use of polynomial spline functions for the solution of system of second order delay differential equations
Ramadan, Mohamed A.
El-Sherbeiny, Abd-El-Aziz
Sherif, Mahmoud N.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2009, 86 (07) : 1167 - 1181
[40] Polynomial spline functions of even degree approximating the solution of differential equations .1.
Micula, G
Blaga, P
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1996, 76 : 477 - 478

← 1 2 3 4 5 →