{"product_id":"9783319427027","title":"An Introductory Guide to Computational Methods for the Solution of Physics Problems: With Emphasis on Spectral Methods","description":"\u003ch1\u003eAn Introductory Guide to Computational Methods for the Solution of Physics Problems: With Emphasis on Spectral Methods\u003c\/h1\u003e \u003ch2\u003eRawitscher, George; dos Santos Filho, Victo; Peixoto, Thiago Carvalho\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003eThis monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally \u003c\/div\u003e\u003cdiv\u003etaught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to \u003c\/div\u003e\u003cdiv\u003ethe solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of \u003c\/div\u003e\u003cdiv\u003eappropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via \u003c\/div\u003e\u003cdiv\u003ecollocation equations. The main advantage of these methods is that they simultaneously take into account all available \u003c\/div\u003e\u003cdiv\u003einformation, rather only the information available at a limited number of mesh points. They require more complicated \u003c\/div\u003e\u003cdiv\u003ematrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the \u003c\/div\u003e\u003cdiv\u003espectral methods more than compensates for anysuch drawbacks. \u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eDuring the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and \u003c\/div\u003e\u003cdiv\u003ethe improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points \u003c\/div\u003e\u003cdiv\u003eused in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solution\u003c\/div\u003e\u003cdiv\u003eof integral equations.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThe monograph includes an informative introduction to old and new computational methods with numerous practical examples, \u003c\/div\u003e\u003cdiv\u003ewhile at the same time pointing out the errors that each of the available algorithms introduces into the specific \u003c\/div\u003e\u003cdiv\u003esolution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students \u003c\/div\u003e\u003cdiv\u003ewishing to compare the available computational methods. In addition, the work develops the criteria required for \u003c\/div\u003e\u003cdiv\u003estudents to select the most suitable method to solve the particular scientific problem that they are confronting.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2018-10-25\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319427027\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-42703-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 221\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":47521115832460,"sku":"9783319427027","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319427027.jpg?v=1776006047","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319427027","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}