{"product_id":"spline-collocation-methods-for-partial-differential-equations-9781119301035","title":"Spline Collocation Methods for Partial","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA comprehensive approach to numerical partial differential equations \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSpline Collocation Methods for Partial Differential Equations \u003c\/i\u003ecombines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions.\u003c\/p\u003e \u003cp\u003eR, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without h\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAbout the CompanionWebsite xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Uniform Grids 2\u003c\/p\u003e \u003cp\u003e1.2 Variable Grids 18\u003c\/p\u003e \u003cp\u003e1.3 Stagewise Differentiation 24\u003c\/p\u003e \u003cp\u003eAppendix A1 – Online Documentation for splinefun 27\u003c\/p\u003e \u003cp\u003eReference 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 One-Dimensional PDEs 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Constant Coefficient 31\u003c\/p\u003e \u003cp\u003e2.1.1 Dirichlet BCs 32\u003c\/p\u003e \u003cp\u003e2.1.1.1 Main Program 33\u003c\/p\u003e \u003cp\u003e2.1.1.2 ODE Routine 40\u003c\/p\u003e \u003cp\u003e2.1.2 Neumann BCs 43\u003c\/p\u003e \u003cp\u003e2.1.2.1 Main Program 44\u003c\/p\u003e \u003cp\u003e2.1.2.2 ODE Routine 46\u003c\/p\u003e \u003cp\u003e2.1.3 Robin BCs 49\u003c\/p\u003e \u003cp\u003e2.1.3.1 Main Program 50\u003c\/p\u003e \u003cp\u003e2.1.3.2 ODE Routine 55\u003c\/p\u003e \u003cp\u003e2.1.4 Nonlinear BCs 60\u003c\/p\u003e \u003cp\u003e2.1.4.1 Main Program 61\u003c\/p\u003e \u003cp\u003e2.1.4.2 ODE Routine 63\u003c\/p\u003e \u003cp\u003e2.2 Variable Coefficient 64\u003c\/p\u003e \u003cp\u003e2.2.1 Main Program 67\u003c\/p\u003e \u003cp\u003e2.2.2 ODE Routine 71\u003c\/p\u003e \u003cp\u003e2.3 Inhomogeneous, Simultaneous, Nonlinear 76\u003c\/p\u003e \u003cp\u003e2.3.1 Main Program 78\u003c\/p\u003e \u003cp\u003e2.3.2 ODE routine 85\u003c\/p\u003e \u003cp\u003e2.3.3 Subordinate Routines 88\u003c\/p\u003e \u003cp\u003e2.4 First Order in Space and Time 94\u003c\/p\u003e \u003cp\u003e2.4.1 Main Program 96\u003c\/p\u003e \u003cp\u003e2.4.2 ODE Routine 101\u003c\/p\u003e \u003cp\u003e2.4.3 Subordinate Routines 105\u003c\/p\u003e \u003cp\u003e2.5 Second Order in Time 107\u003c\/p\u003e \u003cp\u003e2.5.1 Main Program 109\u003c\/p\u003e \u003cp\u003e2.5.2 ODE Routine 114\u003c\/p\u003e \u003cp\u003e2.5.3 Subordinate Routine 117\u003c\/p\u003e \u003cp\u003e2.6 Fourth Order in Space 120\u003c\/p\u003e \u003cp\u003e2.6.1 First Order in Time 120\u003c\/p\u003e \u003cp\u003e2.6.1.1 Main Program 121\u003c\/p\u003e \u003cp\u003e2.6.1.2 ODE Routine 125\u003c\/p\u003e \u003cp\u003e2.6.2 Second Order in Time 138\u003c\/p\u003e \u003cp\u003e2.6.2.1 Main Program 140\u003c\/p\u003e \u003cp\u003e2.6.2.2 ODE Routine 143\u003c\/p\u003e \u003cp\u003eReferences 155\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Multidimensional PDEs 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 2D in Space 157\u003c\/p\u003e \u003cp\u003e3.1.1 Main Program 158\u003c\/p\u003e \u003cp\u003e3.1.2 ODE Routine 163\u003c\/p\u003e \u003cp\u003e3.2 3D in Space 170\u003c\/p\u003e \u003cp\u003e3.2.1 Main Program, Case 1 170\u003c\/p\u003e \u003cp\u003e3.2.2 ODE Routine 174\u003c\/p\u003e \u003cp\u003e3.2.3 Main Program, Case 2 183\u003c\/p\u003e \u003cp\u003e3.2.4 ODE Routine 187\u003c\/p\u003e \u003cp\u003e3.3 Summary and Conclusions 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Navier–Stokes, Burgers’ Equations 197\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 PDE Model 197\u003c\/p\u003e \u003cp\u003e4.2 Main Program 198\u003c\/p\u003e \u003cp\u003e4.3 ODE Routine 203\u003c\/p\u003e \u003cp\u003e4.4 Subordinate Routine 205\u003c\/p\u003e \u003cp\u003e4.5 Model Output 206\u003c\/p\u003e \u003cp\u003e4.6 Summary and Conclusions 208\u003c\/p\u003e \u003cp\u003eReference 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Korteweg–de Vries Equation 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 PDE Model 211\u003c\/p\u003e \u003cp\u003e5.2 Main Program 212\u003c\/p\u003e \u003cp\u003e5.3 ODE Routine 225\u003c\/p\u003e \u003cp\u003eContents ix\u003c\/p\u003e \u003cp\u003e5.4 Subordinate Routines 228\u003c\/p\u003e \u003cp\u003e5.5 Model Output 234\u003c\/p\u003e \u003cp\u003e5.6 Summary and Conclusions 238\u003c\/p\u003e \u003cp\u003eReferences 239\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Maxwell Equations 241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 PDE Model 241\u003c\/p\u003e \u003cp\u003e6.2 Main Program 243\u003c\/p\u003e \u003cp\u003e6.3 ODE Routine 248\u003c\/p\u003e \u003cp\u003e6.4 Model Output 252\u003c\/p\u003e \u003cp\u003e6.5 Summary and Conclusions 252\u003c\/p\u003e \u003cp\u003eAppendix A6.1. Derivation of the Analytical Solution 257\u003c\/p\u003e \u003cp\u003eReference 259\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Poisson–Nernst–Planck Equations 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 PDE Model 261\u003c\/p\u003e \u003cp\u003e7.2 Main Program 265\u003c\/p\u003e \u003cp\u003e7.3 ODE Routine 271\u003c\/p\u003e \u003cp\u003e7.4 Model Output 276\u003c\/p\u003e \u003cp\u003e7.5 Summary and Conclusions 284\u003c\/p\u003e \u003cp\u003eReferences 286\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Fokker–Planck Equation 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 PDE Model 287\u003c\/p\u003e \u003cp\u003e8.2 Main Program 288\u003c\/p\u003e \u003cp\u003e8.3 ODE Routine 293\u003c\/p\u003e \u003cp\u003e8.4 Model Output 295\u003c\/p\u003e \u003cp\u003e8.5 Summary and Conclusions 301\u003c\/p\u003e \u003cp\u003eReferences 303\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Fisher–Kolmogorov Equation 305\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 PDE Model 305\u003c\/p\u003e \u003cp\u003e9.2 Main Program 306\u003c\/p\u003e \u003cp\u003e9.3 ODE Routine 311\u003c\/p\u003e \u003cp\u003e9.4 Subordinate Routine 313\u003c\/p\u003e \u003cp\u003e9.5 Model Output 314\u003c\/p\u003e \u003cp\u003e9.6 Summary and Conclusions 316\u003c\/p\u003e \u003cp\u003eReference 316\u003c\/p\u003e \u003cp\u003e10 Klein–Gordon Equation 317\u003c\/p\u003e \u003cp\u003e10.1 PDE Model, Linear Case 317\u003c\/p\u003e \u003cp\u003e10.2 Main Program 318\u003c\/p\u003e \u003cp\u003e10.3 ODE Routine 323\u003c\/p\u003e \u003cp\u003e10.4 Model Output 326\u003c\/p\u003e \u003cp\u003e10.5 PDE Model, Nonlinear Case 328\u003c\/p\u003e \u003cp\u003e10.6 Main Program 330\u003c\/p\u003e \u003cp\u003e10.7 ODE Routine 335\u003c\/p\u003e \u003cp\u003e10.8 Subordinate Routines 338\u003c\/p\u003e \u003cp\u003e10.9 Model Output 339\u003c\/p\u003e \u003cp\u003e10.10 Summary and Conclusions 342\u003c\/p\u003e \u003cp\u003eReference 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Boussinesq Equation 343\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 PDE Model 343\u003c\/p\u003e \u003cp\u003e11.2 Main Program 344\u003c\/p\u003e \u003cp\u003e11.3 ODE Routine 350\u003c\/p\u003e \u003cp\u003e11.4 Subordinate Routines 354\u003c\/p\u003e \u003cp\u003e11.5 Model Output 355\u003c\/p\u003e \u003cp\u003e11.6 Summary and Conclusions 358\u003c\/p\u003e \u003cp\u003eReferences 358\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Cahn–Hilliard Equation 359\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 PDE Model 359\u003c\/p\u003e \u003cp\u003e12.2 Main Program 360\u003c\/p\u003e \u003cp\u003e12.3 ODE Routine 366\u003c\/p\u003e \u003cp\u003e12.4 Model Output 369\u003c\/p\u003e \u003cp\u003e12.5 Summary and Conclusions 379\u003c\/p\u003e \u003cp\u003eReferences 379\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Camassa–Holm Equation 381\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 PDE Model 381\u003c\/p\u003e \u003cp\u003e13.2 Main Program 382\u003c\/p\u003e \u003cp\u003e13.3 ODE Routine 388\u003c\/p\u003e \u003cp\u003e13.4 Model Output 391\u003c\/p\u003e \u003cp\u003e13.5 Summary and Conclusions 394\u003c\/p\u003e \u003cp\u003e13.6 Appendix A13.1: Second Example of a PDE with a Mixed Partial Derivative 395\u003c\/p\u003e \u003cp\u003e13.7 Main Program 395\u003c\/p\u003e \u003cp\u003e13.8 ODE Routine 398\u003c\/p\u003e \u003cp\u003e13.9 Model Output 400\u003c\/p\u003e \u003cp\u003eReference 403\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Burgers–Huxley Equation 405\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 PDE Model 405\u003c\/p\u003e \u003cp\u003e14.2 Main Program 406\u003c\/p\u003e \u003cp\u003e14.3 ODE Routine 411\u003c\/p\u003e \u003cp\u003e14.4 Subordinate Routine 416\u003c\/p\u003e \u003cp\u003e14.5 Model Output 417\u003c\/p\u003e \u003cp\u003e14.6 Summary and Conclusions 422\u003c\/p\u003e \u003cp\u003eReferences 422\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Gierer–Meinhardt Equations 423\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 PDE Model 423\u003c\/p\u003e \u003cp\u003e15.2 Main Program 424\u003c\/p\u003e \u003cp\u003e15.3 ODE Routine 429\u003c\/p\u003e \u003cp\u003e15.4 Model Output 432\u003c\/p\u003e \u003cp\u003e15.5 Summary and Conclusions 437\u003c\/p\u003e \u003cp\u003eReference 440\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Keller–Segel Equations 441\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 PDE Model 441\u003c\/p\u003e \u003cp\u003e16.2 Main Program 443\u003c\/p\u003e \u003cp\u003e16.3 ODE Routine 449\u003c\/p\u003e \u003cp\u003e16.4 Subordinate Routines 453\u003c\/p\u003e \u003cp\u003e16.5 Model Output 453\u003c\/p\u003e \u003cp\u003e16.6 Summary and Conclusions 458\u003c\/p\u003e \u003cp\u003eAppendix A16.1. Diffusion Models 458\u003c\/p\u003e \u003cp\u003eReferences 459\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Fitzhugh–Nagumo Equations 461\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 PDE Model 461\u003c\/p\u003e \u003cp\u003e17.2 Main Program 462\u003c\/p\u003e \u003cp\u003e17.3 ODE Routine 467\u003c\/p\u003e \u003cp\u003e17.4 Model Output 470\u003c\/p\u003e \u003cp\u003e17.5 Summary and Conclusions 475\u003c\/p\u003e \u003cp\u003eReference 475\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Euler–Poisson–Darboux Equation 477\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 PDE Model 477\u003c\/p\u003e \u003cp\u003e18.2 Main Program 478\u003c\/p\u003e \u003cp\u003e18.3 ODE Routine 483\u003c\/p\u003e \u003cp\u003e18.4 Model Output 488\u003c\/p\u003e \u003cp\u003e18.5 Summary and Conclusions 493\u003c\/p\u003e \u003cp\u003eReferences 493\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Kuramoto–Sivashinsky Equation 495\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 PDE Model 495\u003c\/p\u003e \u003cp\u003e19.2 Main Program 496\u003c\/p\u003e \u003cp\u003e19.3 ODE Routine 503\u003c\/p\u003e \u003cp\u003e19.4 Subordinate Routines 506\u003c\/p\u003e \u003cp\u003e19.5 Model Output 508\u003c\/p\u003e \u003cp\u003e19.6 Summary and Conclusions 513\u003c\/p\u003e \u003cp\u003eReferences 514\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Einstein–Maxwell Equations 515\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 PDE Model 515\u003c\/p\u003e \u003cp\u003e20.2 Main Program 516\u003c\/p\u003e \u003cp\u003e20.3 ODE Routine 521\u003c\/p\u003e \u003cp\u003e20.4 Model Output 526\u003c\/p\u003e \u003cp\u003e20.5 Summary and Conclusions 533\u003c\/p\u003e \u003cp\u003eReference 536\u003c\/p\u003e \u003cp\u003eA Differential Operators in Three Orthogonal Coordinate Systems 537\u003c\/p\u003e \u003cp\u003eReferences 539\u003c\/p\u003e \u003cp\u003eIndex 541\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528852447575,"sku":"9781119301035","price":102.55,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119301035.jpg?v=1731873278","url":"https:\/\/bookcurl.com\/products\/spline-collocation-methods-for-partial-differential-equations-9781119301035","provider":"Book Curl","version":"1.0","type":"link"}