An approximate solution to nonlinear integral equations by the method of invariant imbedding (Q1974753)

For nonlinear integral equations of the Urysohn type \[ Y(t)= \int_a^b F[t,s,Y(s)] ds, \quad t,s\in [a,b], \] where \(F(\cdot)\) is a known nonlinear analytic function with boundary conditions \(Y(a)= Y_a\) and \(Y(b)= Y_b\), the only possible method of solution is the method of successive approximations. The difficulties associated with the practical application of this method are well known. The authors consider a new approach based on the method of invariant imbedding which allows one to substantially reduce the computational expenditure as compared to the method of successive approximations.