## Approximate Methods and Numerical Analysis for Elliptic Complex EquationNumerical methods for elliptic partial differential equations have been the subject of many books in recent years, but few have treated the subject of complex equations. In this important new book, the author introduces the theory of, and approximate methods for, nonlinear elliptic complex equations in multiple connected domains. Constructive methods are systematically applied to proper boundary value problems which include very general boundary conditions. Approximate and numerical methods, such as the Newton imbedding method, the continuity method, the finite element method, the difference method and the boundary integral method, as well as their applications, are discussed in detail. The book will be of interest to all scientists studying the theory or applications of complex analysis. |

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### Contents

Approximate Methods for Solving Elliptic Complex | 45 |

Finite Element Methods for Elliptic Complex Equations | 81 |

Finite Difference Methods for Elliptic Equations | 121 |

Boundary Integral Methods for Elliptic Equations | 151 |

Applications of Approximate Methods and Numerical | 185 |

219 | |

### Common terms and phrases

ahove formula algehraic analytic functions approximate solution Banach space Chapter choose circular domain coefficients complex equation 1.1 continuous functions denote hy derived difference equation elliptic complex equations elliptic equation equa equation of second error estimate exists finite element method following houndary value functions w(z Green's formula harm in assuming harmonic functions hefore Hence Hl(D houndary conditions houndary F houndary value prohlem hounded domain interior node interpolation Lemma linear mapping Math Moreover nonlinear elliptic complex nonnegative constants numerical solutions ohtain Ohviously partial differential equations plane posednesses positive constant Prohlem Bi Prohlem Bz Prohlem H prohlems for elliptic proof of Theorem quasiconformal mapping replaced hy satisfies Condition satisfies the estimates satisfying the condition satisfying the houndary second order Similarly solution of Prohlem solution w(z solvahility of Prohlem solvahle suhstitute Suppose triangular unit uniformly elliptic unique solution variahles vector wn(z