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Numerical solutions of Nagumo’s equation. (English) Zbl 0949.34026

Summary: Nagumo’s equation is the third-order nonlinear ordinary differential equation \[ {d^3u\over dx^3}- c{d^2u\over dx^2}+ f'(u){du\over dx}- (b/c)u= 0 \] with \(f(u)= u(1- u)(u- a)\), \(0< a< 1\). The author develops a technique to determine those values of the parameters \(a\), \(b\) and \(c\) which permit nonconstant bounded solutions.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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