Numerical methods of solving nonlinear integral equations of volterra type

Abstract

519.62 Applying continued fractions, we propose numerical methods of solving nonlinear Volterra integral equations of second kind.Consider a nonlinear Volterra integral equationwhere the function F[x, y, f(y)] has the smoothness needed for the computations. We break the interval It. = [a, b] .. [a+otlh, a+fllh, 0], k2=F[a+et2h, a+fl2h, y21hkl]. dk,l-I +--We determine the parameters aij, ~i, fli (i, j = 1,2) and 1,21 from the condition that the Taylor series expansions of the unknown solution f2 and the approximate solution Y~ 1.0l in a neighborhood of the point x = x l coincide up to terms of order h 2 inclusive.