A NUMERICAL ALGORITHM BASED ON CHEBYSHEV POLYNOMIALS FOR SOLVING SOME INVERSE SOURCE PROBLEMS

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

NEMATI S.; BABAEI A.; SEDAGHAT S.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: MATHEMATICAL RESEARCHES Year:2016 | Volume:2 | Issue:1 Page(s): 47-68

Download Full-Text

Persian Verion

View:

1,226

Download:

140

Cites:

Information Journal Paper

Title

A NUMERICAL ALGORITHM BASED ON CHEBYSHEV POLYNOMIALS FOR SOLVING SOME INVERSE SOURCE PROBLEMS

Author(s)

NEMATI S. | BABAEI A. | SEDAGHAT S. | Issue Writer Certificate

Keywords

PARABOLIC EQUATIONQ2

INVERSE PROBLEMQ2

UNKNOWN SOURCE TERMQ2

TIKHONOV REGULARIZATIONQ2

CHEBYSHEV POLYNOMIALSQ2

OPERATIONAL MATRIXQ1

Abstract

In this paper, two INVERSE PROBLEMs of determining an UNKNOWN SOURCE TERM in a PARABOLIC EQUATION are considered. First, the UNKNOWN SOURCE TERM is estimated in the form of a combination of Chebyshev functions. Then, a numerical algorithm based on CHEBYSHEV POLYNOMIALS is presented for obtaining the solution of the problem. For solving the problem, the operational matrices of integration and derivation are introduced and utilized to reduce the mentioned problem into the matrix equations which correspond to a system of linear algebraic equations with unknown Chebyshev coefficients. Due to ill-posedness of these INVERSE PROBLEMs, the TIKHONOV REGULARIZATION method with generalized cross validation (GCV) criterion is applied to find stable solutions. Finally, some examples are presented to illustrate the efficiency of this numerical method. The numerical results show that the proposed method is a reliable method and can give high accuracy approximate solutions.

Cites

No record.

References

No record.

Cite

APA: Copy

NEMATI, S., BABAEI, A., & SEDAGHAT, S.. (2016). A NUMERICAL ALGORITHM BASED ON CHEBYSHEV POLYNOMIALS FOR SOLVING SOME INVERSE SOURCE PROBLEMS. MATHEMATICAL RESEARCHES, 2(1), 47-68. SID. https://sid.ir/paper/260815/en

Vancouver: Copy

NEMATI S., BABAEI A., SEDAGHAT S.. A NUMERICAL ALGORITHM BASED ON CHEBYSHEV POLYNOMIALS FOR SOLVING SOME INVERSE SOURCE PROBLEMS. MATHEMATICAL RESEARCHES[Internet]. 2016;2(1):47-68. Available from: https://sid.ir/paper/260815/en

IEEE: Copy

S. NEMATI, A. BABAEI, and S. SEDAGHAT, “A NUMERICAL ALGORITHM BASED ON CHEBYSHEV POLYNOMIALS FOR SOLVING SOME INVERSE SOURCE PROBLEMS,” MATHEMATICAL RESEARCHES, vol. 2, no. 1, pp. 47–68, 2016, [Online]. Available: https://sid.ir/paper/260815/en

Related Journal Papers