A method for solving systems of nonlinear Fredholm integral equations. (Chinese. English summary) Zbl 0591.45004
A method for solving the system of nonlinear Fredholm integral equations
\[
\phi (x,\lambda)=f(x)+\int^{b}_{a}\Phi (x,y,\phi (y,\lambda))dy
\]
is discussed, where \(\lambda\) is a sufficiently small parameter, \(\phi\),f,\(\Phi\) are vectors. Using the parameter imbedding method, an equivalent initial value problem for a system of nonlinear coupled integro-differential equations is established. The initial value problem can be reduced to the solution of a system of nonlinear Volterra integral equations which is solvable.
Reviewer: Mingzhong Li
MSC:
45G10 | Other nonlinear integral equations |
45L05 | Theoretical approximation of solutions to integral equations |
45J05 | Integro-ordinary differential equations |