Modeling the Solution of an Ordinary Differential Equation by the Functional Voxel Method

This work discusses an approach to modeling an ordinary differential equation by the Functional Voxel method (FV method). The proposed approach is an automated development of the isocline method and is based on the principles of differentiation and integration developed for FV modeling. The isocline method is analyzed as a mean of constructing a tangential field for solving the first and second order ordinary differential equation. The selected examples demonstrate the principle of constructing a FV model as a basis for obtaining integral curves. An algorithm for obtaining an integral curve of a differential equation by the means of the Functional Voxel modeling is described. A visual and numerical comparative analysis of the obtained results of the FV modeling with known examples is carried out. Unlike the isocline method, where the result is a graphical construction of constant tangent lines, in the case of a Functional voxel model we get a graphical representation of the area of local functions at each point of the integral curve corresponding to the solution of the problem.