scholarly journals Development of the hybrid method to solve boundary values problems in Ordinary Differential equations

2007 ◽  
Vol 19 (3) ◽  
pp. 156-176
Author(s):  
Basheer Al-Hayali ◽  
Mohammed Al-Taee
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Boundary Values

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.

scholarly journals A New L-Stable Third Derivative Hybrid Method for Solving First Order Ordinary Differential Equations

2021 ◽  
pp. 58-69
Author(s):  
Lawrence Osa Adoghe
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Multistep Method ◽  
Stability And Convergence ◽  
Stiff Systems ◽  
Convergence Properties ◽  
Main Method ◽  
The Stability ◽  
Third Derivative

In this paper, an L-stable third derivative multistep method has been proposed for the solution of stiff systems of ordinary differential equations. The continuous hybrid method is derived using interpolation and collocation techniques of power series as the basis function for the approximate solution. The method consists of the main method and an additional method which are combined to form a block matrix and implemented simultaneously. The stability and convergence properties of the block were investigated and discussed. Numerical examples to show the efficiency and accuracy of the new method were presented.

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 A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Sufia Zulfa Ahmad ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Delay Differential Equations ◽  
Scientific Literature ◽  
Second Order ◽  
New Method ◽  
Implicit Methods ◽  
Delay Differential ◽  
Fifth Order

We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

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