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Analytical solution methods for boundary value problems / Anatoly S. Yakimov.

By: Yakimov, A. SMaterial type: TextTextPublication details: London, UK : Academic Press, 2016Description: 1 online resource (202)Content type: text Media type: computer Carrier type: online resourceISBN: 0128043636; 9780128043639Subject(s): Boundary value problems -- Numerical solutions | MATHEMATICS -- Calculus | MATHEMATICS -- Mathematical Analysis | Boundary value problems -- Numerical solutionsGenre/Form: Electronic books.Additional physical formats: Erscheint auch als:: Yakimov, A.S. Analytical Solution Methods for Boundary Value ProblemsDDC classification: 515.4 LOC classification: QA379Online resources: ScienceDirect
Contents:
Front Cover; Analytical Solution Methods for Boundary Value Problems; Copyright; Contents; About the Author; Introduction; Chapter 1: Exact Solutions of Some Linear Boundary Problems; 1.1 Analytical Method of Solution of Three-Dimensional Linear Transfer Equations; Statement of a Problem and a Method Algorithm; Example of Test Calculation; 1.2 The Exact Solution of the First Boundary Problem for Three-Dimensional Elliptic Equations; Statement of a Problem and a Method Algorithm; Application of Integrated Laplace Transformation; Examples of Test Calculation.
Chapter 2: Method of Solution of Nonlinear Transfer Equations2.1 Method of Solution of One-Dimensional Nonlinear Transfer Equations; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Existence; Uniqueness; Estimation of Speed of Convergence [32]; Example of Test Calculation; 2.2 Algorithm of Solution of Three-Dimensional Nonlinear Transfer Equations; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [36]; Results of Test Checks.
Chapter 3: Method of Solution of Nonlinear Boundary Problems3.1 Method of Solution of Nonlinear Boundary Problems; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks; 3.2 Method of Solution of Three-Dimensional Nonlinear First Boundary Problem; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Results of Test Checks; 3.3 Method of Solution of Three-Dimensional Nonlinear Boundary Problems for Parabolic Equation of General Type.
Statement of a Problem and a Method AlgorithmResults of Test Checks; Conclusion; Chapter 4: Method of Solution of Conjugate Boundary Problems; 4.1 Method of Solution of Conjugate Boundary Problems; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks; 4.2 Method of Solution of the Three-Dimensional Conjugate Boundary Problem; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks.
Chapter 5: Method of Solution of Equations in Partial Derivatives5.1 Method of Solution of One-Dimensional Thermal Conductivity Hyperbolic Equation; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks; 5.2 Method of Solution of the Three-Dimensional Equation in Partial Derivatives; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence; Results of Test Checks; Conclusion; Conclusion; Bibliography; Index; Back Cover.
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Print version record.

Front Cover; Analytical Solution Methods for Boundary Value Problems; Copyright; Contents; About the Author; Introduction; Chapter 1: Exact Solutions of Some Linear Boundary Problems; 1.1 Analytical Method of Solution of Three-Dimensional Linear Transfer Equations; Statement of a Problem and a Method Algorithm; Example of Test Calculation; 1.2 The Exact Solution of the First Boundary Problem for Three-Dimensional Elliptic Equations; Statement of a Problem and a Method Algorithm; Application of Integrated Laplace Transformation; Examples of Test Calculation.

Chapter 2: Method of Solution of Nonlinear Transfer Equations2.1 Method of Solution of One-Dimensional Nonlinear Transfer Equations; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Existence; Uniqueness; Estimation of Speed of Convergence [32]; Example of Test Calculation; 2.2 Algorithm of Solution of Three-Dimensional Nonlinear Transfer Equations; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [36]; Results of Test Checks.

Chapter 3: Method of Solution of Nonlinear Boundary Problems3.1 Method of Solution of Nonlinear Boundary Problems; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks; 3.2 Method of Solution of Three-Dimensional Nonlinear First Boundary Problem; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Results of Test Checks; 3.3 Method of Solution of Three-Dimensional Nonlinear Boundary Problems for Parabolic Equation of General Type.

Statement of a Problem and a Method AlgorithmResults of Test Checks; Conclusion; Chapter 4: Method of Solution of Conjugate Boundary Problems; 4.1 Method of Solution of Conjugate Boundary Problems; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks; 4.2 Method of Solution of the Three-Dimensional Conjugate Boundary Problem; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks.

Chapter 5: Method of Solution of Equations in Partial Derivatives5.1 Method of Solution of One-Dimensional Thermal Conductivity Hyperbolic Equation; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence [15, 16]; Results of Test Checks; 5.2 Method of Solution of the Three-Dimensional Equation in Partial Derivatives; Statement of a Problem and a Method Algorithm; Existence, Uniqueness, and Convergence; Estimation of Speed of Convergence; Results of Test Checks; Conclusion; Conclusion; Bibliography; Index; Back Cover.

Includes bibliographical references and index.

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