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x Polynomial Approximation of Differential Equations
10.3 Approximation of linear first-order problems 229
10.4 Nonlinear time-dependent problems 235
10.5 Approximation of the wave equation 237
10.6 Time discretization 243
11. Domain-decomposition methods
11.1 Introductory remarks 249
11.2 Non-overlapping multidomain methods 250
11.3 Solution techniques 260
11.4 Overlapping multidomain methods 263
12. Examples
12.1 A free boundary problem 265
12.2 An example in an unbounded domain 271
12.3 The nonlinear Schrödinger equation 274
12.4 Zeroes of Bessel functions 278
13. An example in two dimensions
13.1 Poisson’s equation 281
13.2 Approximation by the collocation method 282
13.3 Hints for the implementation 287
13.4 The incompressible Navier-Stokes equations 290
References 293
Index 305