Successive approximation method for solving boundary value problems with one-sided nonlinear boundary conditions

Theorem. Let function found in this area and being continuous function and that’s why (6), (7) conditions should be there. If first error (13) select the function vector by zero, then (5) boundary, that is to say the function (1), (2) will be a solution to boundary value problems.

The error between the direct solution and the error solution is estimated by the error equation.

References

1. Samoilenko A.M., Ronto N.I. Numerical-analytical methods

research of solutions to boundary value problems. -Kiev. "Naukova Dumka", 1985. p. 223.

2. Samoilenko A.M., Ronto N.I. Numerical-analytical methods in the theory of boundary value problems of ordinary differential equations. - Kiev: Naukova Dumka, 1992 . 280p.