Partial differential equations : theory, analysis and applications / Christopher L. Jang, editor.

Format:

• Book

Contributor:

• Jang, Christopher L.

Series:

• Mathematics research developments series.
• Mathematics research developments

Language:

English

Subjects (All):

• Differential equations, Partial.
• Mathematical physics.

Physical Description:

1 online resource (357 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2011.

Language Note:

English

Summary:

Partial differential equations are used to formulate and thus aid the solution of problems involving functions of several variables, such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity. This book presents current research in the study of partial differential equations, including a generalized fully spectral weighted residual method (GWRM) for solution of initial value partial differential equations; the Fokker-Planck equation in human population dynamics; solition solutions to one KdV equation; boundary control of systems described by partial differential equations by input-output linearization; the Weierstrass system and partial differential equations as a tool for evaluation of the continuous wavelet transform.

Contents:

• ""PARTIAL DIFFERENTIAL EQUATIONS: THEORY, ANALYSIS AND APPLICATIONS ""; ""PARTIAL DIFFERENTIAL EQUATIONS: THEORY, ANALYSIS AND APPLICATIONS ""; ""CONTENTS ""; ""PREFACE""; ""TIME-SPECTRAL SOLUTION OF INITIAL-VALUE PROBLEMS""; ""ABSTRACT""; ""1. INTRODUCTION ""; ""2. THE METHOD ""; ""2.1. Multivariate Chebyshev Spectral Expansion ""; ""2.2. Weighted Residual Formulation ""; ""2.3. Integration and Differentiation ""; ""2.4. Minimax Considerations ""; ""2.5. Comparison with Least Square WRM Formulation ""; ""3. BOUNDARY AND INITIAL CONDITIONS ""
• ""3.1. Implementation of Boundary and Initial Conditions Chebyshev Approximation """"3.2. Example 1D Diffusion Equation ""; ""4. NONLINEARITY ""; ""5. ROOT SOLVER ""; ""6. SUBDOMAINS""; ""7. APPLICATION - ACCURACY AND EFFICIENCY""; ""7.1. Introductory Example; the Match Equation ""; ""7.2. Accuracy; Burger's Equation""; ""7.2.1. Exact Solution ""; ""7.2.2. GWRM Solution ""; ""7.2.3. Finite Difference Solutions""; ""7.2.4. Internal Gradients""; ""7.3. Efficiency; the Forced Wave Equation ""; ""7.3.1. GWRM Solution""; ""7.3.2. Finite Difference Solutions""
• ""7.3.3. Conclusions on Forced Wave Equation""""7.4. Large System of Initial
• Magnetohydrodynamic Stability ""; ""7.4.1. Benchmarking Using Simplified Model ""; ""7.4.2. GWRM Solution of MHD Stability Problem and Comparison with Eigenvalue Approach ""; ""7.5. Other Systems of Time- ""; ""7.6. Summary - Applications ""; ""8. CONCLUSION ""; ""ACKNOWLEDGMENT ""; ""REFERENCES ""; ""A STOCHASTIC AGENT-BASED APPROACH TO THE FOKKER-PLANCK EQUATION IN HUMAN POPULATION DYNAMICS ""; ""1. INTRODUCTION ""; ""2. THE AGENT-BASED MODEL ""; ""3. THE MAIN RESULT ""; ""4. THE MASTER EQUATION ""
• ""5. THE TRANSFORM OF THE MASTER EQUATION AND PROOF OF LEMMA 4.6 """"ACKNOWLEDGMENT ""; ""REFERENCES ""; ""TRAP-LIMITED DIFFUSION OF HYDROGEN IN AMORPHOUS SILICON THIN FILMS""; ""I. INTRODUCTION""; ""II. CONCEPTS ON DIFFUSION ""; ""II.1. Diffusion through a Fixed Surface ""; ""II.2. Some Special Cases ""; ""II.3. Diffusion through a Moving Surface ""; ""II.4. Trap-Limited Diffusion ""; ""III. EXPERIMENTAL CONDITIONS FOR FILM DEPOSITION AND HYDROGEN PLASMA TREATMENT ""; ""IV. TRAP-LIMITED HYDROGEN DIFFUSING IN AMOURPHOUS SILICON ""
• ""IV.1. Kinetics of Hydrogen Etching of Hydrogenated Amorphous Silicon """"IV.2. Hydrogen Evolution during Microcrystalline Silicon Deposition ""; ""a) Before The Growth of the c-Si:H Layer ( T T1)""; ""b) During the Growth of the c-Si:H Layer ( T > T1) ""; ""c) Hydrogen Out-Diffusion ""; ""REFERENCES ""; ""THE ROLE OF THE METHOD OF CHARACTERISTICS IN THE SOLUTION OF ESTIMATION AND CONTROL PROBLEMS FOR HYPERBOLIC PDE SYSTEMS ""; ""ABSTRACT ""; ""NOMENCLATURE ""; ""ABBREVIATIONS ""; ""1. INTRODUCTION""; ""2. METHOD OF CHARACTERISTICS: BASIC CONCEPTS ""
• ""2.1. Dynamic Systems with One Characteristic Line ""

Notes:

• Description based upon print version of record.
• Includes bibliographical references and index.
• Description based on print version record.

ISBN:

1-61324-743-5

OCLC:

923654883