Titlebook: Computational Physics; Simulation of Classi Philipp O. J. Scherer Textbook 20101st edition Springer-Verlag Berlin Heidelberg 2010 Algorithm

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Theory and Theoretical Framework, importance sampling are introduced. The Metropolis algorithm is studied in detail which is very helpful to calculate thermodynamic averages in configuration space. Computer experiments demonstrate the central limit theorem and nonlinear optimization with the Metropolis method.

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Systems of Inhomogeneous Linear Equationsspecial iterative methods. We discuss the Jacobi and Gauss–Seidel methods and convergence acceleration by the method of successive overrelaxation. Another very efficient method for large systems is the conjugate gradients method which minimizes the gradient of a related quadratic form.

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Error Analysis computer uses only a subset of the real numbers. Input data as well as the results of elementary operations have to be represented by such machine numbers whereby rounding errors can be generated. Results from more complex operations like square roots or trigonometric functions can have even larger

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Interpolation the sampling frequency of audio or video signals, interpolation methods are necessary. But interpolation is also helpful to develop more sophisticated numerical methods for the calculation of numerical derivatives or integrals. Polynomial interpolation is discussed in large detail together with its

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Numerical Differentiation forces from a complicated force field. The simplest method is the explicit forward difference quotient which has a very poor error order. Precision can be improved significantly by using a symmetric difference quotient. Higher order methods are introduced which can be systematically generated with