{"product_id":"9783319427027","title":"An Introductory Guide to Computational Methods for the Solution of Physics Problems: With Emphasis on Spectral Methods","description":"This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally  \u003cbr\u003e taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to  \u003cbr\u003e the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of  \u003cbr\u003e appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via  \u003cbr\u003e collocation equations. The main advantage of these methods is that they simultaneously take into account all available  \u003cbr\u003e information, rather only the information available at a limited number of mesh points. They require more complicated  \u003cbr\u003e matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the  \u003cbr\u003e spectral methods more than compensates for anysuch drawbacks. \u003cbr\u003e  \u003cbr\u003e During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and  \u003cbr\u003e the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points  \u003cbr\u003e used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solution \u003cbr\u003e of integral equations. \u003cbr\u003e  \u003cbr\u003e The monograph includes an informative introduction to old and new computational methods with numerous practical examples,  \u003cbr\u003e while at the same time pointing out the errors that each of the available algorithms introduces into the specific  \u003cbr\u003e solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students  \u003cbr\u003e wishing to compare the available computational methods. In addition, the work develops the criteria required for  \u003cbr\u003e students to select the most suitable method to solve the particular scientific problem that they are confronting. \u003cbr\u003e  \u003cbr\u003e","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":46310363398385,"sku":"9783319427027","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0674\/5433\/7265\/files\/9783319427027_p0.jpg?v=1765171196","url":"https:\/\/shop.barnesandnoble.com\/products\/9783319427027","provider":"Barnes \u0026 Noble","version":"1.0","type":"link"}