Solution to a class of inverse problems for a system of loaded ordinary differential equations with integral conditions

2016 ◽  
Vol 24 (5) ◽  
Author(s):  
Kamil R. Aida-zade ◽  
Vagif M. Abdullayev
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Experiments ◽  
Parametric Identification ◽  
Initial Problem ◽  
Cauchy Problems ◽  
Integral Conditions ◽  
Identification Problems

AbstractThis work is dedicated to the numerical solution of a class of parametric identification problems for dynamic objects. The process is described by a system of loaded ordinary differential equations. Observations over the object have integral (interval) and point characters, at which the results of the observations are given in a summarized non-separated form. We propose a technique that reduces the solution of the initial problem to the solution of specially-built supplementary Cauchy problems. The results of some numerical experiments are also given.

scholarly journals Multivalue Collocation Methods for Ordinary and Fractional Differential Equations

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 185
Author(s):  
Angelamaria Cardone ◽  
Dajana Conte ◽  
Raffaele D’Ambrosio ◽  
Beatrice Paternoster
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Experiments ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Fractional Differential ◽  
Convergence And Stability Analysis

The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for ordinary differential equations, and on two-step spline collocation methods for fractional differential equations. The construction of the methods together with the convergence and stability analysis are reported and some numerical experiments are carried out to show the efficiency of the proposed methods.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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