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Based on Chebyshev’s interpolation theory, the non-homogeneous term of the second-order linear differential equations is interpolated, and a precise integration algorithm with easy programming, high computational efficiency and precision design is realized. The method does not involve inverse operation, and does not need to additionally calculate the matrix index on the integration point, and can control the error boundary based on different precision requirements, so it has high stability and controllability. Numerical examples of periodic loads common in vibration engineering show the effectiveness of the method.

A homogeneous high precision direct integration based on Chebyshev interpolation