Two Conservative Numerical Methods for Solving Initial Value Problems (Global Journal of Science Frontier Research, 2025)
According to the energy conservation equation two novel conservative numerical methods are proposed for solving the second-order initial value problems The C1-continuous piecewise-quadratic functions are also used to approximate the true solutions A priori error estimate is derived under a linear force assumption of the initial value problems Some numerical tests are conducted to verify the theoretical results
Keywords: conservative numerical method; initial value problem; error estimate