The periods and periodic solutions of nonlinear jerk equations solved by an iterative algorithm based on a shape function method

Abstract

The present paper develops two iterative algorithms to determine the periods and then the periodic solutions of nonlinear jerk equations. We consider two possible cases: initial values unknown and initial values given. A shape function method is introduced, by which we can transform the periodic problem to an initial value problem for the new variable, while the period and the terminal values of the new variable at the end of a period are determined iteratively. The initial value problem method (IVPM) can satisfy the periodic conditions exactly. Three examples reveal the advantages of the new iterative algorithms based on the IVPM, which converge fastly and also provide very accurate periodic solutions and periods of the nonlinear jerk equations.