Titlebook: An Introductory Guide to Computational Methods for the Solution of Physics Problems; With Emphasis on Spe George Rawitscher,Victo dos Santo

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Iteratively Calculated Eigenvalues,btain the wave functions required in the procedure can improve the precision to . The numerical application that we present here is again based on the vibration frequencies of an inhomogeneous string as presented in Chap.?.. To close the chapter, we propose a project which applies the method to the case of an exponential attractive potential.

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Convergence of Spectral Approximations,alculation of the interpolation error and the determination of the set of functions that gives rise to the best interpolation in such methods. In last section, we present assignments in order to analyze the rate of convergence and the error of various sets of basis functions in an expansion.

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Chebyshev Polynomials as Basis Functions,val with the smallest error for functions that do not have strong singularities. The convergence of the expansion of functions in terms of Chebyshev polynomials will be illustrated, as well as the accuracy of the calculation of integrals and of derivatives. A novel “hybrid” method for calculating derivatives of higher order will also be described.

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https://doi.org/10.1007/978-3-642-91935-0We also show how these functions serve to obtain a separable representation of a general operator (for example of a non-local potential), and we describe the iterative corrections of the truncation error in a Sturmian expansion.

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Sturmian Functions,We also show how these functions serve to obtain a separable representation of a general operator (for example of a non-local potential), and we describe the iterative corrections of the truncation error in a Sturmian expansion.

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https://doi.org/10.1007/978-3-662-41281-7gorithm is of the Galerkin type. We compare the errors and the speed of calculation of the FE-DVR with those of the S-IEM, where the basis functions are Chebyshev polynomials, and the algorithm is of the Collocation type.