Second-order accurate difference method for the singularly perturbed problem of fourth-order ordinary differential equations
For a class of boundary value problems for ordinary differential equations which are widely applied in mechanics: \(\varepsilon u^{(4)}- (a(x)u)''=f(x)\), \(0<x<1\), \(u(0)=u(1)=0\), \(u''(0)=u''(1)=0\), a uniform second-order difference scheme based on the use of the Petrov-Galerkin finite element method is constructed. A numerical example is given.
scientific article; zbMATH DE number 60168