Download Partial Differential Equations with Fourier Series and by Nakhle H. Asmar PDF

By Nakhle H. Asmar

This example-rich reference fosters a gentle transition from trouble-free traditional differential equations to extra complicated options. Asmar's comfy sort and emphasis on functions make the fabric obtainable even to readers with constrained publicity to subject matters past calculus. Encourages laptop for illustrating effects and functions, yet is usually compatible to be used with out desktop entry. comprises extra engineering and physics purposes, and extra mathematical proofs and conception of partial differential equations, than the 1st version. bargains lots of routines in line with part. offers marginal reviews and comments all through with insightful comments, keys to following the fabric, and formulation recalled for the reader's comfort. bargains Mathematica records to be had for obtain from the author's site. an invaluable reference for engineers or someone who must brush up on partial differential equations.

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Extra info for Partial Differential Equations with Fourier Series and Boundary Value Problems

Example text

15) has a unique solution. We will also discuss how systems of this form can be solved numerically. 13) actually works for a particular case. 5 Let us consider the following two-point boundary value prob- lem: ~u"(x) = (3x + x2)ex, a r e (0,1), w(0) = u(l) = 0, where the exact solution is given by u(x) ~ x{l -x)ex. For this problem, we let bj = h2(3xj + x2)eXj for j — 1,... e. for some values of n. In Fig. 2 we have plotted the exact solution (solid line) and numerical solution (dashed line). For the numerical solution we used n = 5.

The figure shows the numerical solution (dashed line) and the exact solution (solid line) of the boundary value problem. For the numerical scheme, we have used n = 5 interior grid points, and drawn a linear interpolation between the values on the grid. The solution at the grid points are marked by 'o'. 3. The figure shows the numerical solution (dashed line) and the exact solution (solid line) of the boundary value problem. For the numerical scheme, we have used n = 15 interior grid points. 50 2.

61) in Chapter 12. 1 Convergence of Sequences In dealing with numerical approximations of various kinds, we are often interested in assessing the quality of the numerical estimates. Proving error bounds in order to obtain such estimates might be a very difficult task,8 but in many cases empirical estimates can be obtained using simple computer experiments. The purpose of this project is thus to develop a "quick and dirty" way of investigating the convergence of schemes under some fortunate circumstances.

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