A discretization scheme for some conservative problems
For solving differential equations of the form \(m\frac{d^{2} x(t)}{dt^{2}}+h(x(t))=0\) the authors suggest a discretization method with subsequent applying a Newton-like method given by the equalities \[ 0=F(x_{n})+F'(x_{n})(y_{n}-x_{n}), \] \[ 0=F(x_{n})+F(y_{n})+F'(x_{n})(x_{n+1}-x_{n}), \quad n=1,2,3,\dots \]
nonlinear differential equations in Banach space
scientific article; zbMATH DE number 1423317