Two Conservative Numerical Methods for Solving Initial Value Problems
conservative numerical method, initial value problem, error estimate
Abstract
According to the energy conservation equation, two novel conservative numerical methods are proposed for solving the second-order initial value problems. The -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.
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2025-01-20
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