AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS

Huseyin Tunc; Murat Sarı

AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS

Abstract

This paper has proposed a local differential transform method in analysing various types of linear and nonlinear initial value problems (IVP) representing physical models encountered in a broad range of science. Local and global error analyses of the proposed scheme are presented to demonstrate the capacity and priorities of the local differential transform method (LDTM). The produced results show that even using coarser meshes the present scheme produce quite a little error in finite time. The present solution technique in solving the IVPs is compared with the Runge-Kutta method. It is proved that the LDTM produces more accurate results than the Runge-Kutta methods studied in the literature. By considering various types of initial value problems, the stabilities of the LDTM and the RK4 are examined with various time intervals in a comparative way.

Keywords

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Huseyin Tunc This is me
0000-0001-6450-5380
Türkiye

Murat Sarı This is me
0000-0003-0508-2917
Türkiye

Publication Date

March 1, 2019

Submission Date

July 1, 2018

Acceptance Date

November 23, 2018

Published in Issue

Year 2019 Volume: 37 Number: 1

IZ

https://izlik.org/JA84PX75RK

Cite

RIS / Bibtex

APA

Tunc, H., & Sarı, M. (2019). AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS. Sigma Journal of Engineering and Natural Sciences, 37(1), 163-174. https://izlik.org/JA84PX75RK

AMA

1.Tunc H, Sarı M. AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS. SIGMA. 2019;37(1):163-174. https://izlik.org/JA84PX75RK

Chicago

Tunc, Huseyin, and Murat Sarı. 2019. “AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS”. Sigma Journal of Engineering and Natural Sciences 37 (1): 163-74. https://izlik.org/JA84PX75RK.

EndNote

Tunc H, Sarı M (March 1, 2019) AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS. Sigma Journal of Engineering and Natural Sciences 37 1 163–174.

IEEE

[1]H. Tunc and M. Sarı, “AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS”, SIGMA, vol. 37, no. 1, pp. 163–174, Mar. 2019, [Online]. Available: https://izlik.org/JA84PX75RK

ISNAD

Tunc, Huseyin - Sarı, Murat. “AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS”. Sigma Journal of Engineering and Natural Sciences 37/1 (March 1, 2019): 163-174. https://izlik.org/JA84PX75RK.

JAMA

1.Tunc H, Sarı M. AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS. SIGMA. 2019;37:163–174.

MLA

Tunc, Huseyin, and Murat Sarı. “AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 1, Mar. 2019, pp. 163-74, https://izlik.org/JA84PX75RK.

Vancouver

1.Huseyin Tunc, Murat Sarı. AN EFFICIENT LOCAL TRANSFORM METHOD FOR INITIAL VALUE PROBLEMS. SIGMA [Internet]. 2019 Mar. 1;37(1):163-74. Available from: https://izlik.org/JA84PX75RK