Advance in the theory of variable stepsize variable formula methods for ordinary differential equations

The theory of the constant stepsize constant formula methods (CSCFM's) for solving initial value problems for ordinary differential equations (ODE's) is well-developed. However, the integration methods are often used as variable stepsize variable ...

In this paper, a novel, simple yet efficient method is proposed to approximately solve linear ordinary differential equations (ODEs). Emphasis is put on second-order linear ODEs with variable coefficients. First, the ODE to be solved is transformed to ...

When variable stepsize variable formula methods (VSVFM's) are used in the solution of systems of first order differential equations instability arises sometimes. Therefore it is important to find VSVFM's whose zerostability properties are not affected ...