scholarly journals DEGENERATE MATRICES METHODS BY SPLINES FOR BOUNDARY VALUES PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

2005 ◽  
Vol 10 (2) ◽  
pp. 127-140 ◽  
Author(s):  
M. Belovs ◽  
T. Cirulis
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Ordinary Differential Equations ◽  
Boundary Values ◽  
Classical Orthogonal Polynomials ◽  
Initial Values

A method for numerical solving of boundary values problems of ordinary differential equations based on the use of splines and differentiation matrices with nodes as zeroes of classical orthogonal polynomials is considered. Possibilities of the method are shown by means of different examples. The method essentially uses the results obtained by Degenerate Matrices methods and it is applied for solving initial values problems of ordinary differential equations. Darbe nagrinejamas paprastuju lygčiu su kraštinemis salygomis skaitinis sprendimo metodas. Šio metodo pagrinda sudaro nereguliariuju matricu bei splainu konstravimas klasikiniu ortogonaliuju polinomu pavidalu. Nagrinejamo straipsnyje metodo taikymo galimybes parodytos ivairiais pavyzdžiais.

scholarly journals LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL EQUATIONS

1995 ◽  
Vol 10 (24) ◽  
pp. 1795-1802 ◽  
Author(s):  
YURI SMIRNOV ◽  
ALEXANDER TURBINER
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Difference Equations ◽  
Heisenberg Algebra ◽  
Difference Operators ◽  
Discrete Version ◽  
Classical Orthogonal Polynomials ◽  
Finite Difference Equations ◽  
Exactly Solvable

A certain representation for the Heisenberg algebra in finite difference operators is established. The Lie algebraic procedure of discretization of differential equations with isospectral property is proposed. Using sl 2-algebra based approach, (quasi)-exactly-solvable finite difference equations are described. It is shown that the operators having the Hahn, Charlier and Meissner polynomials as the eigenfunctions are reproduced in the present approach as some particular cases. A discrete version of the classical orthogonal polynomials (like Hermite, Laguerre, Legendre and Jacobi ones) is introduced.

scholarly journals Continuous dependence of boundary values for semiinfinite interval ordinary differential equations

1986 ◽  
Vol 9 (3) ◽  
pp. 525-530
Author(s):  
David H. Eberly
Keyword(s):  
Elliptic Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elliptic Equations ◽  
Continuous Dependence ◽  
Boundary Value ◽  
Boundary Values ◽  
Compact Sets

Certain elliptic equations arising in catalysis theory can be transformed into ordinary differential equations on the interval(0,∞). The solutions to these problems usually depend on parametersρ∈ℝn, sayu(t,ρ). For certain types of nonlinearities, we show that the boundary valueu˙(∞,ρ)is continuous on compact sets of the variableρ. As a consequence, bifurcation results for the elliptic equation are obtained.

TESTS IN MATH IN THE MOODLE SYSTEM: PRODUCTION OF ANSWERS FOR QUIZZES IN ORDINARY DIFFERENTIAL EQUATIONS 2

2020 ◽  
Author(s):  
Наталья Валентиновна Майгула ◽  
Юрий Николаевич Марасанов ◽  
Данил Арменович Сумбатян
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Values

Демонстрируются методы решения математических задач в пакете Symbolic Math Toolbox системы компьютерной математики MATLAB. В данной работе рассматриваются задачи по дифференциальным уравнениям 2-го порядка и выше: проверка заданного решения, отыскание общего и частных решений уравнения, решение задач Коши и краевых задач. The production of answers for math quizzes is discussed. The problems in ODE of the 2nd order and above are solved (verifying and finding solutions, solving initial and boundary values problems). MATLAB Symbolic Math Toolbox is a tool.

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