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Preface; Digital Art by Walid Ben Medjedel; Contents; List of Contributors; 1 An L1-Product-Integration Method in Astrophysics; 1.1 Introduction; 1.2 A Product-Integration Method in C; 1.3 Iterative Refinement; 1.4 Numerical Evidence; References; 2 Differential Operators and Approximation Processes Generated by Markov Operators; 2.1 Introduction; 2.2 Canonical Elliptic Second-Order Differential Operators and Bernstein-Schnabl Operators; 2.3 Other Classes of Differential Operators and Approximation Processes; 2.4 Final Remarks; References
3 Analysis of Boundary-Domain Integral Equations for Variable-Coefficient Neumann BVP in 2D3.1 Preliminaries; 3.2 Parametrix-Based Potential Operators; 3.3 BDIEs for Neumann BVP; 3.4 Equivalence and Invertibility Theorems; 3.5 Perturbed BDIE Systems for the Neumann Problem; 3.6 Conclusion; References; 4 A Measure of the Torsional Performances of Partially Hinged Rectangular Plates; 4.1 Introduction; 4.2 Variational Setting and Gap Function Definition; 4.3 Proof of Theorem 1; 4.4 Proof of Theorem 2; 4.5 Proofs of Theorems 3 and 4; References
5 On a Class of Integral Equations Involving Kernels of Cosine and Sine Type5.1 Introduction; 5.2 Integral Equations Generated by an Integral Operator with Cosine and Sine Kernels; 5.3 Operator Properties; 5.3.1 Invertibility and Spectrum; 5.3.2 Parseval-Type Identity and Unitary Properties; 5.3.3 Involution; 5.3.4 New Convolution; References; 6 The Simple-Layer Potential Approach to the Dirichlet Problem: An Extension to Higher Dimensions of Muskhelishvili Method and Applications; 6.1 Introduction; 6.2 Muskhelishvili's Method and Its Extension to Rn; 6.2.1 Muskhelishvili's Method
6.2.2 Conjugate Differential Forms6.2.3 The Extension to Higher Dimensions of Muskhelishvili Method; 6.3 The Multiple-Layer Approach; References; 7 Bending of Elastic Plates: Generalized Fourier Series Method; 7.1 Introduction; 7.2 The Boundary Value Problem; 7.3 Numerical Example; 7.4 Graphical Illustrations; 7.5 The Classical Gram-Schmidt Procedure (CGS); 7.6 The Modified Gram-Schmidt Procedure (MGS); 7.7 The Householder Reflection Procedure (HR); References; 8 Existence and Uniqueness Results for a Class of Singular Elliptic Problems in Two-Component Domains; 8.1 Introduction
8.2 Setting of the Problem8.3 A Priori Estimates; 8.4 Main Results; References; 9 Fredholmness of Nonlocal Singular Integral Operators with Slowly Oscillating Data; 9.1 Introduction; 9.2 Invertibility Criteria for Wiener Type Functional Operators; 9.3 Mellin Pseudodifferential Operators; 9.4 Fredholmness of the Operator N; References; 10 Multidimensional Time Fractional Diffusion Equation; 10.1 Introduction; 10.2 Preliminaries; 10.3 Fundamental Solution of the Multidimensional Time Fractional Diffusion-Wave Equation; 10.4 Fractional Moments
3 Analysis of Boundary-Domain Integral Equations for Variable-Coefficient Neumann BVP in 2D3.1 Preliminaries; 3.2 Parametrix-Based Potential Operators; 3.3 BDIEs for Neumann BVP; 3.4 Equivalence and Invertibility Theorems; 3.5 Perturbed BDIE Systems for the Neumann Problem; 3.6 Conclusion; References; 4 A Measure of the Torsional Performances of Partially Hinged Rectangular Plates; 4.1 Introduction; 4.2 Variational Setting and Gap Function Definition; 4.3 Proof of Theorem 1; 4.4 Proof of Theorem 2; 4.5 Proofs of Theorems 3 and 4; References
5 On a Class of Integral Equations Involving Kernels of Cosine and Sine Type5.1 Introduction; 5.2 Integral Equations Generated by an Integral Operator with Cosine and Sine Kernels; 5.3 Operator Properties; 5.3.1 Invertibility and Spectrum; 5.3.2 Parseval-Type Identity and Unitary Properties; 5.3.3 Involution; 5.3.4 New Convolution; References; 6 The Simple-Layer Potential Approach to the Dirichlet Problem: An Extension to Higher Dimensions of Muskhelishvili Method and Applications; 6.1 Introduction; 6.2 Muskhelishvili's Method and Its Extension to Rn; 6.2.1 Muskhelishvili's Method
6.2.2 Conjugate Differential Forms6.2.3 The Extension to Higher Dimensions of Muskhelishvili Method; 6.3 The Multiple-Layer Approach; References; 7 Bending of Elastic Plates: Generalized Fourier Series Method; 7.1 Introduction; 7.2 The Boundary Value Problem; 7.3 Numerical Example; 7.4 Graphical Illustrations; 7.5 The Classical Gram-Schmidt Procedure (CGS); 7.6 The Modified Gram-Schmidt Procedure (MGS); 7.7 The Householder Reflection Procedure (HR); References; 8 Existence and Uniqueness Results for a Class of Singular Elliptic Problems in Two-Component Domains; 8.1 Introduction
8.2 Setting of the Problem8.3 A Priori Estimates; 8.4 Main Results; References; 9 Fredholmness of Nonlocal Singular Integral Operators with Slowly Oscillating Data; 9.1 Introduction; 9.2 Invertibility Criteria for Wiener Type Functional Operators; 9.3 Mellin Pseudodifferential Operators; 9.4 Fredholmness of the Operator N; References; 10 Multidimensional Time Fractional Diffusion Equation; 10.1 Introduction; 10.2 Preliminaries; 10.3 Fundamental Solution of the Multidimensional Time Fractional Diffusion-Wave Equation; 10.4 Fractional Moments