A Compendium of Partial Differential Equation Models presents numerical methods and associated computer codes in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs), one of the mostly widely used forms of mathematics in science and engineering. The authors focus on the method of lines (MOL), a well-established numerical procedure for all major classes of PDEs in which the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and thus makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code as related to the associated equations of the PDE model.
A Compendium of Partial Differential Equation Models
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"The book may provide a useful collection of most of the classical evolution equations in one spatial dimension together with a summary of their important properties, and numerical illustrations for those who seek an overview without the usual mathematical rigor."
Othmar Koch, Mathematical Reviews
Othmar Koch, Mathematical Reviews
Book Description
A Compendium of Partial Differential Equation Models presents numerical methods and associated computer codes in Matlab for the solution of a spectrum of models expressed as ordinary and partial differential equations (ODE/PDEs), one of the mostly widely used forms of mathematics in science and engineering. The authors focus on the well-established method of lines, making the code easy to understand, implement, and modify.
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First Sentence:
The chapters in this book pertain particularly to mathematical models expressed as partial differential equations (PDEs). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
diffusion equation, linear partial differential equation, plot type, order elseif, following points about this program, end uint, stagewise differentiation, axis tight title, output fprintf, order tenth order, increment calls, end fprintf, nonstiff integrator, simp computes, following points about this output, integrator returns, front sharpening, principal error term, analytical solutions figure, shading interp, matrix conversion, previous simulation run, usual transpose, infinite spatial domain, plotted output Key Phrases - Capitalized Phrases (CAPs): (learn more)
Compendium of Partial Differential Equation Models, Spherical Coordinates, Navier Stokes, Cylindrical Coordinates, Green's Function Analysis, Laplace's Equation, The Linear Wave Equation, The Cubic Schrödinger Equation, New York, Animating Simulation Results, Burgers Equations, Two Nonlinear, Maxwell's Equations, Implementation of Time-Varying, Conservation Principles, Boca Raton, Term Units, Color Plate Section, Analytical Solution of Nonlinear, Academic Press, San Diego, Lecture Notes, Cambridge University Press, Principles of Computational Fluid Dynamics, Num Anal Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
The chapters in this book pertain particularly to mathematical models expressed as partial differential equations (PDEs). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
diffusion equation, linear partial differential equation, plot type, order elseif, following points about this program, end uint, stagewise differentiation, axis tight title, output fprintf, order tenth order, increment calls, end fprintf, nonstiff integrator, simp computes, following points about this output, integrator returns, front sharpening, principal error term, analytical solutions figure, shading interp, matrix conversion, previous simulation run, usual transpose, infinite spatial domain, plotted output Key Phrases - Capitalized Phrases (CAPs): (learn more)
Compendium of Partial Differential Equation Models, Spherical Coordinates, Navier Stokes, Cylindrical Coordinates, Green's Function Analysis, Laplace's Equation, The Linear Wave Equation, The Cubic Schrödinger Equation, New York, Animating Simulation Results, Burgers Equations, Two Nonlinear, Maxwell's Equations, Implementation of Time-Varying, Conservation Principles, Boca Raton, Term Units, Color Plate Section, Analytical Solution of Nonlinear, Academic Press, San Diego, Lecture Notes, Cambridge University Press, Principles of Computational Fluid Dynamics, Num Anal Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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