ARC-length method for differential equations

An arc_length method is presented to solve the ordinary differential equations (ODEs) with certain types of singularity such as stiff property or discontinuity on continuum problem. By introducing one or two arc_length parameters as variables, the differential equations with singularity are transformed into non_singularity equations, which can be solved by usual methods. The method is also applicable for partial differential equations (PDEs), because they may be changed into systems of ODEs by discretization. Two examples are given to show the accuracy, efficiency and application.