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.

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.

POST ADAPTATION FOR A NUMERICAL SOLUTION OF THE SPHERICALLY-SYMMETRIC RIEMANN PROBLEM

1990 ◽  
Vol 01 (04) ◽  
pp. 285-298
Author(s):  
B. YUDANIN ◽  
M. LAX
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Riemann Problem ◽  
General Purpose ◽  
Spherically Symmetric ◽  
Lagrangian Coordinates ◽  
Point Boundary ◽  
Boundary Values

A"folding" transformation is used to reduce a two point boundary value problem to one point boundary values (with double the number of functions). A transformation to quasi-Lagrangian coordinates is used to transform discontinuities to rest. After these transformations the general purpose numerical package POST (partial and ordinary differential equations solver in time and one space coordinates) can be successfully applied to a system of hydrodynamical equations, whose solution exhibits jumps and cusp-type discontinuities. Numerical results are presented for the spherically-symmetric shock problem.

scholarly journals On the Stability of Solutions of Linear Boundary Value Problems for a System of Ordinary Differential Equations

1994 ◽  
Vol 1 (2) ◽  
pp. 115-126
Author(s):  
M. Ashordia
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
Linear Boundary ◽  
Boundary Values ◽  
Small Perturbations ◽  
The Stability ◽  
Stability Of The Solution

Abstract Linear boundary value problems for a system of ordinary differential equations are considered. The stability of the solution with respect to small perturbations of coefficients and boundary values is investigated.

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.

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