The Integral Equation, Corresponding to the Ordinary Differential Equation ()
Abstract
The differential operator of the ordinary differential equation (ODE) is represented as the sum of two operators: basic and supplementing operators. The order of the higher derivatives of a basic operator and ODE operator should coincide. If the basic operator has explicit system of fundamental solutions it is possible to make integral equation Volterra of II kind. For linear equations the approximate solutions of the integral equation are system of the approximate fundamental solutions of the initial ODE.
Share and Cite:
Dobrovolsky, I. (2014) The Integral Equation, Corresponding to the Ordinary Differential Equation.
Open Access Library Journal,
1, 1-5. doi:
10.4236/oalib.1101058.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
Верлань, А.Ф. and Сизиков, В.С. (1986) Интегральные уравнения. Методы. Алгоритмы. Наукова думка, Киев, 543 с.
http://dx.doi.org/10.1016/j.acha.2014.04.002
|
|
[2]
|
Corona, E., Martinsson, P.-G. and Zorin, D. (2014) An O(N) Direct Solver for Integral Equations on the Plane. Applied and Computational Harmonic Analysis.
|
|
[3]
|
Shang, Y. (2013) The Limit Behavior of a Stochastic Logistic Model with Individual Time-Dependent Rates. Journal of Mathematics, 2013, Article ID: 502635.
|
|
[4]
|
Zhang, W.G., Bai, X.J., Sun, X.F., Cai, G.Y., Bai, X.Y., Zhu, S.Y., Zhang, M. and Chen, X.M. (2014) Construction of an Integral Formula of Biological Age for a Healthy Chinese Population Using Principle Component Analysis. Journal of Nutrition, Health, and Aging, 18, 137-142.
http://dx.doi.org/10.1007/s12603-013-0345-8
|
|
[5]
|
Pathak, H.K., Khan, M.S. and Tiwari, R. (2007) A Common Fixed Point Theorem and Its Application to Nonlinear Integral Equations. Computers and Mathematics with Applications, 53, 961-971.
http://dx.doi.org/10.1016/j.camwa.2006.08.046
|
|
[6]
|
Shang, Y. (2011) Likelihood Estimation for Stochastic Epidemics with Heterogeneous Mixing Populations. World Academy of Science, Engineering and Technology, 55, 929-933.
|