Numerical solutions of nonstandard first order initial value problems

[摘要] Differential equations of the formy′=f(t,y,y′), wherefis not necessarily linear in its arguments, represent certain physical phenomena and are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier, we established the existence of a (unique) solution of the nonstandard initial value problem (NSTD IV P)y′=f(t,y,y′),y(t0)=y0under certain natural hypotheses onf. In this paper we present some first order convergent numerical methods for finding the approximate solutions of the NST D I V Ps.

[学科分类] 应用数学