A family of numerical methods for the solution of high-order general initial value problems
A family of numerical methods is developed for the solution of the general initial value problem \(y^{(N)}(t)=f(t,y,y',...,y^{(N-1)})\), \(t>t_ 0\), with \(y(t_ 0)\), \(y^{(r)}(t_ 0)\) given \((r=1,2,...,N- 1)\). The orders of the methods are seen to be one or two and global extrapolation is used to increase the order of a given method by one or two powers. The methods are tested on the Blasius nonlinear third-order initial value problem and on a linear fourth-order problem from ship dynamics.
Blasius nonlinear third-order initial value problem
scientific article; zbMATH DE number 4005479