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An Introduction to Partial Differential Equations by Jacob Rubinstein, Yehuda Pinchover

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11

Numerical methods

11.1 Introduction

In the previous chapters we studied a variety of solution methods for a large number of PDEs. We point out, though, that the applicability of these methods is limited to canonical equations in simple domains. Equations with nonconstant coefficients, equations in complicated domains, and nonlinear equations cannot, in general, be solved analytically. Even when we can produce an ‘exact’ analytical solution, it is often in the form of an infinite series. Worse than that, the computation of each term in the series, although feasible in principle, might be tedious in practice, and, in addition, the series might converge very slowly. We shall therefore present in this chapter an entirely different approach to ...

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