The Two-sided FD-method of Solving the First Boundary Problem for Singular ODE of the Second Order in the Half-axis

V.L. Makarov, I.I. Lazurchak
2002 Computational Methods in Applied Mathematics  
To solve the boundary problems for singular ordinary differential equations of the second order the functional-discrete (FD-) method is proposed. The method gives the possibility of obtaining an approximate solution in the numerical-analytical form in the whole half-axis with a guaranteed accuracy. Sufficient conditions of convergence of the method at a rate of a geometrical progression are found. The two-sided approximations are established and an explicit evaluation of the two-sided
more » ... two-sided estimation width is given. In conclusion the results of numerical experiments obtained by the system of computer algebra are presented.
doi:10.2478/cmam-2002-0016 fatcat:jxj6j2ua4bc6jjobaqtsjmfy74