| Preface | p. v |
| Exterior Problems of Partial Differential Equations | p. 1 |
| Harmonic equation-potential theory | p. 2 |
| Poisson equations | p. 12 |
| Poisson equations-variational formulation | p. 13 |
| Helmholtz equations | p. 17 |
| Linear elasticity | p. 25 |
| Bi-harmonic equations | p. 29 |
| Steady-Navier-Stokes equations -linearized problems | p. 35 |
| Navier-Stokes equations | p. 35 |
| Stokes equations | p. 36 |
| Behavior of solutions at the infinity | p. 39 |
| Stokes paradox | p. 41 |
| Oseen flow | p. 41 |
| Steady Navier-Stokes equations | p. 44 |
| Heat equation | p. 49 |
| Wave equation | p. 53 |
| Maxwell equations | p. 56 |
| Darwin model | p. 61 |
| Boundary Element Method | p. 71 |
| Some typical domains | p. 71 |
| Harmonic equation | p. 71 |
| Bi-harmonic equation | p. 75 |
| Stokes equation | p. 77 |
| Plane elasticity | p. 80 |
| Helmholtz equation | p. 82 |
| General domains | p. 85 |
| Subdivision of the domain | p. 93 |
| Dirichlet to Neumann operator | p. 96 |
| Finite part of divergent integrals | p. 98 |
| Numerical approximation | p. 103 |
| Error estimates | p. 108 |
| Domain decomposition | p. 113 |
| Boundary perturbation | p. 114 |
| Infinite Element Method | p. 117 |
| Harmonic equation-two dimensional problems | p. 117 |
| Infinite element formulation | p. 117 |
| Tranfer matrix | p. 120 |
| Further discussion for the transfer matrix | p. 127 |
| Combined stiffness matrix | p. 131 |
| General elements | p. 133 |
| Harmonic equation-three dimensional problems | p. 134 |
| Inhomogeneous equations | p. 136 |
| Plane elasticity | p. 138 |
| Bi-harmonic equations | p. 140 |
| Stokes equation | p. 142 |
| Darwin model | p. 147 |
| Elliptic equations with variable coefficients | p. 152 |
| A homogeneous equation | p. 152 |
| An inhomogeneous equation | p. 155 |
| General multiply connected domains | p. 158 |
| Transfer matrices | p. 161 |
| Convergence | p. 162 |
| Artificial Boundary Conditions | p. 167 |
| Absorbing boundary conditions | p. 167 |
| Some approximations | p. 172 |
| Bayliss-Turkel radiation boundary conditions | p. 175 |
| A lower order absorbing boundary condition | p. 176 |
| Liao extrapolation in space and time | p. 178 |
| Maxwell equations | p. 178 |
| Finite difference schemes | p. 182 |
| Stationary Navier-Stokes equations | p. 183 |
| Homogeneous boundary condition at the infinity | p. 183 |
| Inhomogeneous boundary conditions at the infinity | p. 186 |
| A linear boundary condition | p. 187 |
| Perfectly Matched Layer Method | p. 191 |
| Wave equations | p. 191 |
| Berenger's perfectly matched layers | p. 197 |
| Stability analysis | p. 201 |
| Uniaxial perfectly matched layers | p. 208 |
| Maxwell equations | p. 210 |
| Helmholtz equations | p. 212 |
| Spectral Method | p. 217 |
| Introduction | p. 217 |
| Orthogonal systems of polynomials | p. 225 |
| Laguerre spectral methods | p. 230 |
| Mixed Laguerre-Fourier spectral method | p. 230 |
| Spherical harmonic-generalized Laguerre spectral method | p. 235 |
| Generalized Laguerre pseudo-spectral method | p. 237 |
| Nonlinear equations | p. 239 |
| Jacobi spectral methods | p. 241 |
| Rational and irrational spectral methods | p. 243 |
| Error estimates | p. 245 |
| Bibliography | p. 251 |
| Index | p. 265 |
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