Issue: 2(7), 2008. Series: Multi-Topic

Method and Algorithm for the solution of essentially nonlinear ordinary integro-differential equations

UDK: 517.968.74

Bandurin N. G., Ignat'ev V. A.

Basing on the procedure of polynomial interpolation suggested by the author earlier integration and differentiation formulas were obtained.  The integration formula expresses the values of function and its derivatives in the points of segment division through the values of highest-order derivative in these points and the values of function and low-order derivatives in the initial point.  The differentiation formula expresses the values of derivatives in the points of segment division through the values of function in these points and the values of derivatives in the initial point. Applying the integration formula the authors describe  an algorithm and a program for numerical solution of the systems of correct  mild in general case essentially nonlinear ordinary integro-differential equations (IDE), containing integrals with constant and/or variable superior limits, the integrands of which in their turn may depend on the “internal” integrals with constant and/or variable superior limits. The issues of the initial estimate choice and iteration process convergence for general case are not discussed. The developed computer program for PC works in unattended mode, that is, to get the computation results one should enter only the texts of the equations and integrands in the regular form, as well as the problem’s numerical parameters into the computer memory. The paper gives the results of the solution of three sample problems.