Nonlinear Integral Equations
Integral equations appear in many engineering and physics problems. Numerical methods of solution for integral equations have been largely developed within the last 20 years (References 1–4). In this chapter a development involving an imbedding method for obtaining the numerical solution of nonlinear integral equations is described (References 5, 6). The numerical solution is obtained automatically from the initial value imbedding equations via the automatic derivative evaluation method described in the previous chapters (Reference 7). The derivatives required for the solution are computed automatically. The user need only enter the two known functions in equation (6.1) into the program. None of the derivatives associated with the imbedding method need be derived by hand. The subroutines are written in Basic here, rather than in Fortran, because the former has several advantages in the manipulation of the vectors and matrices which occur in using the method of lines. The vectors consisting of the variables or functions of the variables, and all their derivatives are defined as derivative vectors (instead of just vectors) in this chapter to distinguish them from the other vectors and matrices.
KeywordsIntegral Equation Quadrature Formula Fredholm Integral Equation Nonlinear Integral Equation Grid Interval
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