Introduction to numerical ordinary and partial differential equations using MATLAB
Learn how to solve complex differential equations using MATLAB Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB teaches readers how to numerically solve both ordinary and partial differential equations with ease. This innovative publication brings together a skillful treatment of MATLAB and programming alongside theory and modeling. By presenting these topics in tandem, the author enables and encourages readers to perform their own computer experiments, leading them to a more profound understanding of differential equations. The text consists of three parts: Introduction to MATLAB and numerical preliminaries, which introduces readers to the software and itsgraphical capabilities and shows how to use it to write programs Ordinary Differential Equations Partial Differential Equations All the tools needed to master using MATLAB to solve differential equations are provided and include: "Exercises for the Reader" that range from routine computations to more advanced conceptual and theoretical questions (solutions appendix included) Illustrative examples, provided throughout the text, that demonstrate MATLAB's powerful ability to solve differential equations Explanations that are rigorous, yet written in a very accessible, user-friendly style Access to an FTP site that includes downloadable files of all the programs developed in the text This textbook can be tailored for courses in numerical differential equations and numerical analysis as well as traditional courses in ordinary and/or partial differential equations. All the material has been classroom-tested over the course of many years, with the result that any self-learner with an understanding of basic single-variable calculus can master this topic. Systematic use is made of MATLAB's superb graphical capabilities to display and analyze results. An extensive chapter on the finite element method covers enough practical aspects (including mesh generation) to enable the reader to numerically solve general elliptic boundary value problems. With its thorough coverage of analytic concepts, geometric concepts, programs and algorithms, and applications, this is an unsurpassed pedagogical tool.
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Basic Concepts of Numerical Analysis
Introduction to MFiles
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algorithm approximation augmented matrix bisection method coefﬁcient matrix compute condition number convergence corresponding create default deﬁned deﬁnition derivatives det(A differential equations eigenvalues eigenvectors equilibrium solution Euler method exact solution example Exercise Figure ﬁnal ﬁnd ﬁnite difference method ﬁrst ﬁrst-order ﬂoating point arithmetic ﬂoating point number ﬂow fonn fonnula formula fractal function M-ﬁle Gauss-Seidel Gaussian elimination give graph graphic grid points homogeneous coordinates inﬁnite initial conditions inline function input variables interval leﬁ linear system loop mathematical MATLAB multiplication Newton's method Newton’s method nonsingular nonzero norm notation number of iterations numerical solution numerical stability obtain ofthe orbit output variables parameter phase-plane plot population positive integer reader real number root Runge-Kutta method satisﬁes scheme secant method solve speciﬁed square step size h syntax Taylor polynomial Taylor's theorem triangle vertices wave y-coordinates zero