Abstract
The state equations of the linear dynamic system with initial or boundary value conditions are solved by an effective shifted Legendre polynomials approximation. A powerful calculation algorithm is proposed to integrate the state equation with very accurate results as time tends to infinity. A recursive formula is developed to calculate the expansion coefficients of the state functions for saving computer time and minimizing the computational error. The proposed method is very suitable to solve a class of problems with peculiar control functions such as periodic functions or piecewise discontinuous functions. Several illustrative examples are given. Satisfactory computational results are obtained.
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