Numerical expansion methods for solving systems of linear integral equations using interpolation and quadrature rules

References

• Green , C. D. 1969 . Integral Equation Methods , New York : Nelson .
   Google Scholar
• Kanwal , R. P. 1996 . Linear Integral Equations Theory and Technique , Boston : Springer .
   Google Scholar
• Atkinson , K. E. 1997 . The Numerical Solution of the Second Kind , Cambridge : Cambridge University Press .
   Google Scholar
• Delves , L. M. and Mohamed , J. L. 1985 . Computational Methods for Integral Equations , Cambridge : Cambridge University Press .
   Google Scholar
• Golberg , M. A. 1990 . “ Numerical Solution of Integral Equations ” . In Mathematical Concepts and Methods in Science and Engineering , Edited by: Golberg , M. A. Vol. 42 , New York : Plenum .
   Google Scholar
• Wazwaz , A. M. 1997 . First Course in Integral Equations , Edited by: Wazwaz , A. M. Singapore : WSPS .
   Google Scholar
• Maleknejad , K. and Lotfi , T. 2005 . Numerical expansion methods for solving integral equations by interpolation and Gauss quadrature rules . Applied Mathematics and Computation , 168 : 111 – 124 .
   Google Scholar
• Sezer , M. and Doğan , S. 1996 . Chebyshev series solutions of Fredholm integral equations . International Journal of Mathematical Education in Science and Technology , 27 : 649 – 657 .
   Google Scholar
• Rashed , M. T. 2004 . Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations . Applied Mathematics and Computation , 151 : 869 – 878 .
   Web of Science ®Google Scholar
• Rashed , M. T. 2004 . Numerical solution of functional differential, integral and integro-differential equations . Applied Mathematics and Computation , 156 : 485 – 492 .
   Google Scholar
• Maleknejad , K. , Tavassoli Kajani , M. and Mahmoudi , Y. 2003 . Numerical solution of linear Fredholm and Volterra integral equation of the second kind by using Legendre wavelets . Kybernetes , 32 : 1530 – 1539 .
   Web of Science ®Google Scholar
• Maleknejad , K. and Derili , H. 2006 . Numerical solution of integral equations by using combination of Spline-collocation method and Lagrange interpolation . Applied Mathematics and Computation , 175 : 1235 – 1244 .
   Google Scholar
• Wazwaz , A. M. and Khuri , S. A. 1996 . A reliable technique for solving the weakly singular second-kind Volterra-type integral equations . Applied Mathematics and Computation , 80 : 287 – 299 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 1999 . A reliable modification of Adomian decomposition method . Applied Mathematics and Computation , 102 : 77 – 86 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 2006 . A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations . Applied Mathematics and Computation , 181 : 1703 – 1712 .
   Web of Science ®Google Scholar
• Maleknejad , K. and Shahrezaee , M. 2004 . Using Runge–Kutta method for numerical solution of the system of Volterra integral equation . Applied Mathematics and Computation , 149 : 399 – 410 .
   Web of Science ®Google Scholar
• Akyüz-Daşçioğlu , A. 2004 . Chebyshev polynomial solutions of systems of linear integral equations . Applied Mathematics and Computation , 151 : 221 – 232 .
   Web of Science ®Google Scholar
• Maleknejad , K. and Mirzaee , F. 2003 . Numerical solution of linear Fredholm integral equations system by rationalized Haar functions method . International Journal of Computer Mathematics , 80 : 1397 – 1405 .
   Web of Science ®Google Scholar
• Babolian , E. and Biazar , J. 2000 . Solution of a system of nonlinear volterra equations of the second kind . Far East Journal of Mathematical Science , 2 : 935 – 945 .
   Google Scholar
• Babolian , E. , Biazar , J. and Vahidi , A. R. 2004 . On the decomposition method for system of linear equations and system of linear Volterra integral equations . Applied Mathematics and Computation , 147 : 19 – 27 .
   Web of Science ®Google Scholar
• Babolian , E. , Biazar , J. and Vahidi , A. R. 2004 . The decomposition method applied to systems of Fredholm integral equations of the second kind . Applied Mathematics and Computation , 148 : 443 – 452 .
   Web of Science ®Google Scholar
• Biazar , J. , Babolian , E. and Islam , R. 2003 . Solution of a system of Volterra integral equations of the first kind by Adomian method . Applied Mathematics and Computation , 139 : 249 – 258 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 2003 . The existence of noise terms for systems of inhomogeneous differential and integral equations . Applied Mathematics and Computation , 146 : 81 – 92 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 2005 . The modified decomposition method for analytic treatment of non-linear integral equations and systems of non-linear integral equations . International Journal of Computer Mathematics , 82 : 1107 – 1115 .
   Web of Science ®Google Scholar
• Clenshaw , C. W. and Curtis , A. R. 1960 . A method for numerical integration on an automatic computer . Numerische Mathematik , 2 : 197 – 205 .
   Google Scholar
• Davis , P. J. 1975 . Interpolation and Approximation , New York : Dover .
   Google Scholar
• Fox , L. and Parker , I. B. 1968 . Chebyshev Polynomials in Numerical Analysis , Oxford : Oxford University Press . Oxford Mathematical Handbooks
   Google Scholar
• Wazwaz , A. M. 2002 . A reliable treatment for mixed Volterra–Fredholm integral equations . Applied Mathematics and Computation , 127 : 405 – 414 .
   Web of Science ®Google Scholar