Application of the Taylor differential transformation for solving the integro-differential equations

• Autorzy: Grzymkowski, R. , Pleszczyński, M.
• Języki publikacji: EN

Abstrakty

EN

A method of solving the integro-differential equations is presented. The discussed equations will be solved by the Taylor differential transformation. By using appropriate properties of this transformation the integro-differential equation will be transformed to a respective recurrence equation. Unfortunately, the high degree of generality and complexity of such defined problem does not allow to obtain the solution in general form. Each equation requires a special method of solution.

Słowa kluczowe

PL

transformata Taylora; równanie różniczkowe zwyczajne; równanie różniczkowo-całkowe; równanie całkowe

EN

Taylor transformation; ordinary differential equations; integro-differential equations; integral equations

• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2018
• Tom: Vol. 8, iss. 1
• Strony: 33--48
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Grzymkowski, R.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland,

autor

Pleszczyński, M.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

Bibliografia

• 1. Biazar J., Eslami M., Islam M.R.: Differential transform method for special systems of integral equations. J. King Saud Univ. – Sci. 24 (2012), 211–214.
• 2. Dŏgan N., Ertürk V.S., Momani S., Akın Ö., Yildirim A.: Differential transform method for solving singularly perturbed Volterra integral equations. J. King Saud Univ. – Sci. 23 (2011), 223–228.
• 3. Gliński H., Grzymkowski R., Kapusta A., Słota D.: Mathematica 8. Jacek Skalmierski Computer Studio, Gliwice 2012 (in Polish).
• 4. Grzymkowski R.: Taylor transformation and its applications. Jacek Skalmierski Computer Studio, Gliwice 2015 (in Polish).
• 5. Grzymkowski R., Hetmaniok E., Pleszczyński M.: A novel algorithm for solving the ordinary differential equations. In: Selected Problems on Experimental Mathematics, E. Hetmaniok, D. Słota, T. Trawiński, R. Wituła (eds.), Silesian University of Technology Press, Gliwice 2017, 103–112.
• 6. Grzymkowski R., Hetmaniok E., Pleszczyński M.: The Taylor transformation hybrid method applied for solving the Stefan problem. Silesian J. Pure Appl. Math. 6 (2016), 111–123.
• 7. Grzymkowski R., Pleszczyński M.: Application of the Taylor transformation to the systems of ordinary differential equations. The 24th International Conference on Information and Software Technologies (ICIST 2018), Lithuania (2018), in press.
• 8. Grzymkowski R., Pleszczyński M., Hetmaniok E.: Application of the Taylor differential transformation in the calculus of variations. Silesian J. Pure Appl. Math. 7 (2017), 65–82.
• 9. Odibat Z.M.: Differential transform method for solving Volterra integral equation with separable kernels. Math. Comput. Model. 48 (2008), 1144–1149.
• 10. Ravi Kanth A.S.V., Aruna K.: Differential transform method for solving the linear and nonlinear Klein-Gordon equation. Compu. Phys. Comm. 185 (2009), 708–711.
• 11. Ravi Kanth A.S.V., Aruna K., Chaurasia R.K.: Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations. J. King Saud Univ. – Eng. Sci. 29 (2017), 166–171.
• 12. Srivastava V.K., Awasthi M.K.: Differential transform method for solving linear and non-linear systems of partial differential equations. Phys. Lett. A 372 (2008), 6896–6898.
• 13. Tari A., Shahmorad S.: Differential transform method for the system of twodimensional nonlinear Volterra integro-differential equations. Comput. Math. Appl. 61 (2011), 2621–2629.
• 14. Wolfram S.: An Elementary Introduction to the Wolfram Language, Second Edition. Wolfram Media, Champaign 2017.
• 15. Wolfram S.: The Mathematica Book. Fifth Edition. Wolfram Media, Champaign 2003.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW
przeznaczonych na działalność upowszechniającą naukę (2019).