Nonlinear partial differential equations in engineering : Volume 2 Front Cover; Nonlinear Partial Differential Equations in Engineering; Copyright Page; Contents; Preface; Contents of Volume I; Chapter 1. Analytic Techniques and Solutions; 1.0 Introduction; 1.1 Nonlinear Superposition Principles; 1.2 Generation of Nonlinear Equations with Built in Solutions; 1.3 Employing the Wrong Equation to Find the Right Solution; 1.4 Application of the Quasi Linear Theory; 1.5 Earnshaws Procedure; 1.6 Traveling Wave Solutions; 1.7 Arbitrary Functions; 1.8 Equation Splitting; 1.9 Inversion of Dependent and Independent Variables; 1.10 Contact Transformations 2.14 Transformation of Boundary Value Problems into Initial Value Problems Simultaneous EquationsReferences; Chapter 3. Approximate Methods; 3.0 Introduction; 3.1 Weighted Residual Methods (WRM); 3.2 Novel Applications of WRM in Fluid Mechanics; 3.3 WRM in Transport Phenomena Some Recent Literature; 3.4 WRM in Dynamics and Solid Mechanics; 3.5 Comments on WRM Theory; 3.6 Maximum Principles Ordinary Differential Equations; 3.7 Maximum Principles Partial Differential Equations; 3.8 Quasi Linearization; 3.9 Regular Perturbation and Irregular Domains; 3.10 Classical Regular Perturbation In this book we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low rank 2.4 Incorporation of the Auxiliary Conditions2.5 Determination of Absolute Invariants; 2.6 Example of Deductive Similarity Method; 2.7 Similarity Formalism with Multiparameter Groups; 2.8 Infinitesimal Transformations; 2.9 Classical Determination of Infinitesimal Transformations; 2.10 Nonclassical Determination of Infinitesimal Transformations; 2.11 The Nonclassical Method and Simultaneous Equations; 2.12 Some Similarity Literature; 2.13 Transformation of Boundary Value Problems into Initial Value Problems Single Equations 3.11 The Perturbation Method of Keller et al3.12 Singular Perturbation; 3.13 Lighthills Method of Strained Coordinates; 3.14 Miscellaneous Asymptotic Procedures; References; Chapter 4. Numerical Methods; 4.0 Introduction; A. Finite Elements; 4.1 Introduction to Finite Elements; 4.2 Formulation of Finite Element Characteristics; 4.3 Theoretical Comments on Displacement Functions; 4.4 Additional Elements in Two and Three Dimensions; 4.5 Finite Elements and Field Problems; 4.6 Finite Elements and Nonlinear Problems; B. Numerical Solutions in Fluid Mechanics; 4.7 Preliminary Remarks 1.11 Parametrization and the Legendre Transformation1.12 Bäcklund Transformations; 1.13 An Example Bäcklund Transformation; 1.14 First Integrals; 1.1 5 Development of First Integrals; 1.16 Lagrange Series Solutions; 1.17 Breakdown Theory of Jeffrey Lax; 1.18 Application of the Jeffrey Lax Method; 1.19 Dynamics of Moving Threadline; 1.20 Ballooning Vibration of a Moving Threadline; References; Chapter 2. Applications of Modern Algebra; 2.0 Introduction; 2.1 The Similarity Method of Morgan; 2.2 Application of the Morgan Method; 2.3 Determination of Groups by Finite Transformations