The combination of modified Simpson and Newton-Kantrovich methods for solving nonlinear integral equations
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In this work, we apply the combination of Newton Kan- torovich method and modi ed Simpson method for to solve numerically the nonlinear integral equations Volterra or Fredholm. This method transforms the nonlinear integral equations to a linear integral equations of the second kind which will be solved by modi eed Simpson method. This late lead to a system of algebraic equations. Thus, by solving the matrix equation, the coe¢ cients are obtained. A numeri- cal example is included to certify the validity and applicability of the proposed technique.
Abstract
In this work, we apply the combination of Newton Kan- torovich method and modi ed Simpson method for to solve numerically the nonlinear integral equations Volterra or Fredholm. This method transforms the nonlinear integral equations to a linear integral equations of the second kind which will be solved by modi eed Simpson method. This late lead to a system of algebraic equations. Thus, by solving the matrix equation, the coe¢ cients are obtained. A numeri- cal example is included to certify the validity and applicability of the proposed technique.
참고문헌 (6)
- A. V. Manzhirov, "Handbook of integral equation" (2008), Taylor & Francis Group
- J. Saberi-Nadja, "Solving nonlinear integral equations in the Urysohn form by Newton Kantorovich quadrature method", Computers and Mathematics with Applications, 60, pp.2058~2065 (2010)
- F. G. Tricomi, "Integral equations" (1957), University of Press
- A. M. Wazwaz, "Linear and nonlinear integral equations methods and applications" (2011), Press, Beijing and Springer-Verlag
- R. Precup, "Methods in nonlinear integral equations" (2002), Springer-Science +Business Media Dordrecht
- M. Nadir, "Modi ed method for solving linear Volterra integral equations of second kind", IJMM, pp.141~146 (2007)