NUMERICAL INTEGRATION OF FIRST-ORDER STIFF DIFFERENTIAL EQUATIONS

1966 ◽  
Author(s):  
F. C. LOPER ◽  
W. J. Phares
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Stiff Differential Equations ◽  
First Order

Numerical Kinematical Analysis of the Shaping Mechanism

2019 ◽  
Vol 17 (17) ◽  
pp. 37-49
Author(s):  
Vladimir Dragoş Tătaru ◽  
Mircea Bogdan Tătaru
Keyword(s):  
Differential Equations ◽  
Machine Tool ◽  
Numerical Integration ◽  
Reference System ◽  
First Order ◽  
Kinematical Analysis ◽  
Machine Tool Structure ◽  
Numerical Integration Methods ◽  
Linear Differential ◽  
Kinematical Parameters

AbstractThe paper deals with the complete kinematical analysis of the mechanism that enters the machine tool structure designed to generate, in particular, plane surfaces. A machine tool of this kind is called shaping machine. For this purpose, Euler’s relations concerning the velocities distribution, written in projections on the fix reference system axes will be used. Starting from these relations we will get to a system of the first order linear differential equations whose unknowns are the kinematical parameters of the mechanism elements. The variation in time of these parameters will be obtained by solving the differential equations system the differential equations system using numerical integration methods.

scholarly journals A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations

2020 ◽  
Vol 12 (1) ◽  
pp. 72-82
Author(s):  
Solomon Gebregiorgis ◽  
Hailu Muleta
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Multistep Method ◽  
Stiff Differential Equations ◽  
Block Method ◽  
Initial Value ◽  
Numerical Examples ◽  
First Order

In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method.  Keywords: Power series, Collocation, Interpolation, Block method, Stiff.

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