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Trigonometrically-Fitted Methods: A Review
Numerical methods for the solution of ordinary differential equations are based on polynomial interpolation. In 1952, Brock and Murray have suggested exponentials for the case that the solution is known to be of exponential type. In 1961, Gautschi came up with the idea of using information on the frequency of a solution to modify linear multistep methods by allowing the coefficients to depend on the frequency. Thus the methods integrate exactly appropriate trigonometric polynomials. This wasdoi:10.3390/math7121197 fatcat:dvultq7hobez3ajfiktjkwqqju