An adaptive wavelet method for nonlinear differential-algebraic equations

A multi-resolution collocation method with specially designed spline wavelet is presented to numerically solve a system of nonlinear differential-algebraic equations of index one in circuit simulation. As the wavelet collocation method is applied to such system, we will have to solve large nonlinear algebraic equations. For the algebraic equations, we give a modified Newton type iterative method which bases on two wavelet adaptive techniques. We prove the convergence, the stability and the complexity on the adaptive method reported here. The new approach could effectively reduce computational costs and storage requirements to large extent. Numerical experiments are given to further illustrate the method’s principle.