THE NUMERICAL SOLUTION OF FREDHOLM-HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MESHLESS METHOD

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ASSARI POURIA; Adibi Hojatollah; Dehghan mehdi

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

Seminar Paper

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Seminar: ANNUAL IRANIAN MATHEMATICS CONFERENCE
Year:2013 | Issue:44

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Title

THE NUMERICAL SOLUTION OF FREDHOLM-HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MESHLESS METHOD

Author(s)

ASSARI POURIA | Adibi Hojatollah | Dehghan mehdi | Issue Writer Certificate

Keywords

FREDHOLM-HAMMERSTEIN INTEGRAL EQUATION

MOVING LEAST SQUARES (MLS) APPROXIMATION

MESHLESS METHOD

DISCRETE COLLOCATION METHOD

Abstract

IN THIS PAPER, WE PRESENT A COMPUTATIONAL METHOD FOR SOLVING FREDHOLM-HAMMERSTEIN INTEGRAL EQUATIONS OF THE SECOND KIND. THE METHOD UTILIZES SHAPE FUNCTIONS OF THE MOVING LEAST SQUARES (MLS) APPROXIMATION CONSTRUCTED ON SCATTERED POINTS AS A BASIS IN THE DISCRETE COLLOCATION METHOD. THE MLS METHODOLOGY IS AN EFFECTIVE TECHNIQUE FOR THE APPROXIMATION OF AN UNKNOWN FUNCTION AND CONSISTS OF A LOCAL WEIGHTED LEAST SQUARE FITTING, VALID ON A SMALL NEIGHBORHOOD OF A POINT. THE PROPOSED METHOD IS A MESH LESS METHOD, SINCE IT DOES NOT REQUIRE ANY BACKGROUND INTERPOLATION OR APPROXIMATION CELLS. THE PROPOSED SCHEME IS SIMPLE AND COMPUTATIONALLY ATTRACTIVE. FINALLY, A NUMERICAL EXAMPLE IS PRESENTED TO ILLUSTRATE THE EFFICIENCY AND ACCURACY OF THE NEW TECHNIQUE.

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APA: Copy

ASSARI, POURIA, Adibi, Hojatollah, & Dehghan, mehdi. (2013). THE NUMERICAL SOLUTION OF FREDHOLM-HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MESHLESS METHOD. ANNUAL IRANIAN MATHEMATICS CONFERENCE. SID. https://sid.ir/paper/924569/en

Vancouver: Copy

ASSARI POURIA, Adibi Hojatollah, Dehghan mehdi. THE NUMERICAL SOLUTION OF FREDHOLM-HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MESHLESS METHOD. 2013. Available from: https://sid.ir/paper/924569/en

IEEE: Copy

POURIA ASSARI, Hojatollah Adibi, and mehdi Dehghan, “THE NUMERICAL SOLUTION OF FREDHOLM-HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MESHLESS METHOD,” presented at the ANNUAL IRANIAN MATHEMATICS CONFERENCE. 2013, [Online]. Available: https://sid.ir/paper/924569/en

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