APPLICATION OF THE EXACT OPERATIONAL MATRICES FOR SOLVING THE EMDEN-FOWLER EQUATIONS, ARISING IN ASTROPHYSICS

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HOSSAYNI S.A.; RAD J.A.; PARAND K.; ABBASBANDY S.

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Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2015 | Volume:7 | Issue:4 Page(s): 351-374

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Title

APPLICATION OF THE EXACT OPERATIONAL MATRICES FOR SOLVING THE EMDEN-FOWLER EQUATIONS, ARISING IN ASTROPHYSICS

Author(s)

HOSSAYNI S.A. | RAD J.A. | PARAND K. | ABBASBANDY S. | Issue Writer Certificate

Keywords

EXACT OPERATIONAL MATRICESQ2

BERNSTEIN POLYNOMIALSQ2

EMDEN-FOWLER EQUATIONQ2

LANE-EMDEN EQUATIONQ2

Abstract

The objective of this paper is applying the well-known EXACT OPERATIONAL MATRICES (EOMs) idea for solving the EMDEN-FOWLER EQUATIONs, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the excellence of this new method. So, we chose Emden-Fowler type differential equations and solved them utilizing this method. To confirm the accuracy of the new method and to show the preeminence of EOMs over OOMs, the norm 1 of the residual and error function for both methods are evaluated for multiple m values, where m is the degree of the BERNSTEIN POLYNOMIALS. We report the results by some plots to illustrate the error convergence of both methods to zero and also to show the primacy of the new method versus OOMs. The obtained results demonstrate the increased accuracy of the new method.

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APA: Copy

HOSSAYNI, S.A., RAD, J.A., PARAND, K., & ABBASBANDY, S.. (2015). APPLICATION OF THE EXACT OPERATIONAL MATRICES FOR SOLVING THE EMDEN-FOWLER EQUATIONS, ARISING IN ASTROPHYSICS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 7(4), 351-374. SID. https://sid.ir/paper/231697/en

Vancouver: Copy

HOSSAYNI S.A., RAD J.A., PARAND K., ABBASBANDY S.. APPLICATION OF THE EXACT OPERATIONAL MATRICES FOR SOLVING THE EMDEN-FOWLER EQUATIONS, ARISING IN ASTROPHYSICS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2015;7(4):351-374. Available from: https://sid.ir/paper/231697/en

IEEE: Copy

S.A. HOSSAYNI, J.A. RAD, K. PARAND, and S. ABBASBANDY, “APPLICATION OF THE EXACT OPERATIONAL MATRICES FOR SOLVING THE EMDEN-FOWLER EQUATIONS, ARISING IN ASTROPHYSICS,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 7, no. 4, pp. 351–374, 2015, [Online]. Available: https://sid.ir/paper/231697/en

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