Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations

A Chebyshev collocation method, an expansion method, has been proposed in order to solve the systems of higher-order linear integro-differential equations. This method transforms the IDE system and the given conditions into the matrix equations via Chebyshev collocation points. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Chebyshev coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the systems of differential and integral equations.

[1]  M. Sezer,et al.  Chebyshev polynomial solutions of linear differential equations , 1996 .

[2]  Stuart Crozier,et al.  Caluculating Current Densities and Fields Produced by Shielded Magnetic Resonance Imaging Probes , 1997, SIAM J. Appl. Math..

[3]  W. H. Enright,et al.  Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay , 1997 .

[4]  L. Delves,et al.  Computational methods for integral equations: Frontmatter , 1985 .

[5]  Christopher T. H. Baker,et al.  A perspective on the numerical treatment of Volterra equations , 2000 .

[6]  Aysegül Akyüz-Dascioglu,et al.  Chebyshev polynomial solutions of systems of linear integral equations , 2004, Appl. Math. Comput..

[7]  Mehmet Sezer,et al.  A Taylor Collocation Method for the Solution of Linear Integro-Differential Equations , 2002, Int. J. Comput. Math..

[8]  C. W. Clenshaw,et al.  A method for numerical integration on an automatic computer , 1960 .

[9]  Mehmet Sezer,et al.  Chebyshev polynomial solutions of systems of high-order linear differential equations with variable coefficients , 2003, Appl. Math. Comput..

[10]  Ben P. Sommeijer,et al.  Euler-Chebyshev methods for integro-differential equations , 1997 .

[11]  M. A. Abdou.  Fredholm-Volterra integral equation of the first kind and contact problem , 2002, Appl. Math. Comput..

[12]  K. Holmåker.  Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones , 1993 .

[13]  Frederick Bloom,et al.  Asymptotic bounds for solutions to a system of damped integrodifferential equations of electromagnetic theory , 1979 .

[14]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

[15]  Peter Linz,et al.  Analytical and numerical methods for Volterra equations , 1985, SIAM studies in applied and numerical mathematics.

[16]  Khosrow Maleknejad,et al.  Solving linear integro-differential equation system by Galerkin methods with hybrid functions , 2004, Appl. Math. Comput..

[17]  Farshid Mirzaee,et al.  Solving linear integro-differential equations system by using rationalized Haar functions method , 2004, Appl. Math. Comput..