{"title":"Frank Stenger","description":null,"products":[{"product_id":"navierstokes-equations-on-r3-0-t-book-frank-stenger-9783319275246","title":"Navier–Stokes Equations on R3 × [0, T]","description":"\u003cp\u003eIn this monograph, leading researchers in the world of\nnumerical analysis, partial differential equations, and hard computational\nproblems study the properties of solutions of the Navier–Stokes\u003cb\u003e \u003c\/b\u003epartial differential equations on (x, y, z,\nt) ∈ ℝ\u003csup\u003e3\u003c\/sup\u003e × [0, \u003ci\u003eT\u003c\/i\u003e]. Initially converting the PDE to a\nsystem of integral equations, the authors then describe spaces \u003cb\u003eA\u003c\/b\u003e of analytic functions that house\nsolutions of this equation, and show that these spaces of analytic functions\nare dense in the spaces \u003ci\u003eS\u003c\/i\u003e of rapidly\ndecreasing and infinitely differentiable functions. This method benefits from\nthe following advantages:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eThe functions of S are\n     nearly always conceptual rather than explicit\u003c\/li\u003e\n\u003cli\u003eInitial and boundary\n     conditions of solutions of PDE are usually drawn from the applied sciences,\n     and as such, they are nearly always piece-wise analytic, and in this case,\n     the solutions have the same properties\u003c\/li\u003e\n\u003cli\u003eWhen methods of\napproximation are applied to functions of \u003cb\u003eA\u003c\/b\u003e they converge at an exponential rate, whereas methods of\n     approximation applied to the functions of \u003cb\u003eS\u003c\/b\u003e converge only at a polynomial rate\u003c\/li\u003e\n\u003cli\u003eEnables sharper bounds on\n     the solution enabling easier existence proofs, and a more accurate and\n     more efficient method of solution, including accurate error bounds\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\n\n\n\n\u003c\/p\u003e\u003cp\u003eFollowing the proofs of denseness, the authors prove the\nexistence of a solution of the integral equations in the space of functions \u003cb\u003eA\u003c\/b\u003e ∩ ℝ\u003csup\u003e3\u003c\/sup\u003e × [0, \u003ci\u003eT\u003c\/i\u003e], and provide an explicit novel\nalgorithm based on Sinc approximation and Picard–like iteration for computing\nthe solution. Additionally, the authors include appendices that provide a\ncustom Mathematica program for computing solutions based on the explicit\nalgorithmic approximation procedure, and which supply explicit illustrations of\nthese computed solutions.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52473502073105,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52473503777041,"sku":"NLS9783319275246","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319275246.jpg?v=1785772434"},{"product_id":"handbook-of-sinc-numerical-methods-book-frank-stenger-9781138116177","title":"Handbook of Sinc Numerical Methods","description":"Reflecting the author's advances with Sinc since 1995, this handbook contains roughly 450 MATLAB (R) programs for approximating almost every type of operation stemming from calculus. It also presents new and powerful methods for solving ordinary differential equations, partial differential equations, and integral equations. The book makes Sinc meth","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52474400702737,"sku":"NLS9781138116177","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53368590500113,"sku":"NIN9781138116177","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781138116177.jpg?v=1786100206"},{"product_id":"navierstokes-equations-on-r3-0-t-book-frank-stenger-9783319801629","title":"Navier–Stokes Equations on R3 × [0, T]","description":"\u003cp\u003eIn this monograph, leading researchers in the world of\nnumerical analysis, partial differential equations, and hard computational\nproblems study the properties of solutions of the Navier–Stokes\u003cb\u003e \u003c\/b\u003epartial differential equations on (x, y, z,\nt) ∈ ℝ\u003csup\u003e3\u003c\/sup\u003e × [0, \u003ci\u003eT\u003c\/i\u003e]. Initially converting the PDE to a\nsystem of integral equations, the authors then describe spaces \u003cb\u003eA\u003c\/b\u003e of analytic functions that house\nsolutions of this equation, and show that these spaces of analytic functions\nare dense in the spaces \u003ci\u003eS\u003c\/i\u003e of rapidly\ndecreasing and infinitely differentiable functions. This method benefits from\nthe following advantages:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eThe functions of S are\n     nearly always conceptual rather than explicit\u003c\/li\u003e\n\u003cli\u003eInitial and boundary\n     conditions of solutions of PDE are usually drawn from the applied sciences,\n     and as such, they are nearly always piece-wise analytic, and in this case,\n     the solutions have the same properties\u003c\/li\u003e\n\u003cli\u003eWhen methods of\napproximation are applied to functions of \u003cb\u003eA\u003c\/b\u003e they converge at an exponential rate, whereas methods of\n     approximation applied to the functions of \u003cb\u003eS\u003c\/b\u003e converge only at a polynomial rate\u003c\/li\u003e\n\u003cli\u003eEnables sharper bounds on\n     the solution enabling easier existence proofs, and a more accurate and\n     more efficient method of solution, including accurate error bounds\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\n\n\n\n\u003c\/p\u003e\u003cp\u003eFollowing the proofs of denseness, the authors prove the\nexistence of a solution of the integral equations in the space of functions \u003cb\u003eA\u003c\/b\u003e ∩ ℝ\u003csup\u003e3\u003c\/sup\u003e × [0, \u003ci\u003eT\u003c\/i\u003e], and provide an explicit novel\nalgorithm based on Sinc approximation and Picard–like iteration for computing\nthe solution. Additionally, the authors include appendices that provide a\ncustom Mathematica program for computing solutions based on the explicit\nalgorithmic approximation procedure, and which supply explicit illustrations of\nthese computed solutions.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52584265056529,"sku":"NLS9783319801629","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783319801629.jpg?v=1785980162"},{"product_id":"numerical-methods-based-on-sinc-and-analytic-functions-book-frank-stenger-9781461276371","title":"Numerical Methods Based on Sinc and Analytic Functions","description":"Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52617042886929,"sku":"NLS9781461276371","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461276371.jpg?v=1785979782"},{"product_id":"handbook-of-sinc-numerical-methods-book-frank-stenger-9781439821589","title":"Handbook of Sinc Numerical Methods","description":"\u003cp\u003e\u003cstrong\u003eHandbook of Sinc Numerical Methods\u003c\/strong\u003e presents an ideal road map for handling general numeric problems. Reflecting the author’s advances with Sinc since 1995, the text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to scientists and engineers. This new theory, which combines Sinc convolution with the boundary integral equation (IE) approach, makes for exponentially faster convergence to solutions of differential equations. The basis for the approach is the Sinc method of approximating almost every type of operation stemming from calculus via easily computed matrices of very low dimension.\u003c\/p\u003e\u003cp\u003eThe downloadable resources of this handbook contain roughly 450 MATLAB® programs corresponding to exponentially convergent numerical algorithms for solving nearly every computational problem of science and engineering. While the book makes Sinc methods accessible to users wanting to bypass the complete theory, it also offers sufficient theoretical details for readers who do want a full working understanding of this exciting area of numerical analysis. \u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53795191587089,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":53795191750929,"sku":"NLS9781439821589","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781439821589.jpg?v=1789817484"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-frank-stenger.oembed","provider":"World of Books ","version":"1.0","type":"link"}