AN ITERATIVE SCHEME FOR NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS USING COLLOCATION METHOD AND CHEBYSHEV POLYNOMIALS

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RASHIDINIA JALIL; NAJAFI ESMAEIL; ARZHANG ASGHAR

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ISSN: 2588-4824

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Journal: MATHEMATICAL SCIENCES Year:2012 | Volume:6 | Issue:- Page(s): 1-10

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Title

AN ITERATIVE SCHEME FOR NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS USING COLLOCATION METHOD AND CHEBYSHEV POLYNOMIALS

Author(s)

RASHIDINIA JALIL | NAJAFI ESMAEIL | ARZHANG ASGHAR | Issue Writer Certificate

Keywords

VOLTERRA INTEGRAL EQUATIONS

QUASILINEAR TECHNIQUE

COLLOCATION METHOD

CHEBYSHEV POLYNOMIALS

Abstract

When we discretize nonlinear VOLTERRA INTEGRAL EQUATIONS using some numerical, such as COLLOCATION METHODs, the arising algebraic systems are nonlinear. Applying QUASILINEAR TECHNIQUE to the nonlinear VOLTERRA INTEGRAL EQUATIONS gives raise to linear VOLTERRA INTEGRAL EQUATIONS. The solutions of these equations yield a functional sequence quadratically convergent to the solution. Then, we use COLLOCATION METHOD based on CHEBYSHEV POLYNOMIALS and a modified Clenshaw-Curtis quadrature and obtain a numerical solution. Error analysis has been performed, and the method has been applied on three numerical examples.

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APA: Copy

RASHIDINIA, JALIL, NAJAFI, ESMAEIL, & ARZHANG, ASGHAR. (2012). AN ITERATIVE SCHEME FOR NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS USING COLLOCATION METHOD AND CHEBYSHEV POLYNOMIALS. MATHEMATICAL SCIENCES, 6(-), 1-10. SID. https://sid.ir/paper/322614/en

Vancouver: Copy

RASHIDINIA JALIL, NAJAFI ESMAEIL, ARZHANG ASGHAR. AN ITERATIVE SCHEME FOR NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS USING COLLOCATION METHOD AND CHEBYSHEV POLYNOMIALS. MATHEMATICAL SCIENCES[Internet]. 2012;6(-):1-10. Available from: https://sid.ir/paper/322614/en

IEEE: Copy

JALIL RASHIDINIA, ESMAEIL NAJAFI, and ASGHAR ARZHANG, “AN ITERATIVE SCHEME FOR NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS USING COLLOCATION METHOD AND CHEBYSHEV POLYNOMIALS,” MATHEMATICAL SCIENCES, vol. 6, no. -, pp. 1–10, 2012, [Online]. Available: https://sid.ir/paper/322614/en

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