A course on integral equations with numerical analysis : advanced numerical analysis / / Tofigh Allahviranloo, Armin Esfandiari

• Autore: Allahviranloo Tofigh
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (222 pages)
• Disciplina: 515.45
• Soggetto topico: Integral equations; Numerical analysis
• Persona (resp. second.): EsfandiariArmin
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction to Numerical Analysis -- 1.1 Introduction -- 1.2 Error Analysis -- 1.2.1 Errors in an Algorithm -- 1.2.2 Round of Error and Floating Points Arithmetic -- 1.2.3 Algorithm Error Propagation -- 1.3 Interpolation -- 1.3.1 Lagrange Interpolation -- 1.3.2 Newton's Divided Difference Interpolation -- 1.4 A Short Review on Vector Norms and Linear System of Equations -- 1.4.1 Vector Norm -- 1.4.2 Direct Methods -- 1.4.3 Numerical Methods -- 1.5 Numerical Integration -- 1.5.1 Newton-Cotes Integration Method -- 1.5.2 The Peano's Kernel Representation -- 1.5.3 Gauss Integration Method -- 2 Interval Interpolation -- 2.1 Interval Error -- 2.1.1 Interval Calculations -- 2.2 Interval Interpolation -- 2.2.1 Theorem -- 2.2.2 Theorem -- 2.2.3 Theorem -- 2.2.4 Example -- 2.2.5 Example -- 3 Orthogonal Polynomials and Least Square Approximation -- 3.1 Orthogonal Polynomials -- 3.1.1 Definition-Inner Product of Definite Functions -- 3.1.2 Definition-Orthogonal Functions -- 3.1.3 Example -- 3.1.4 Example -- 3.1.5 Example -- 3.1.6 Definition -- 3.1.7 Example -- 3.1.8 Theorem -- 3.1.9 Orthogonal Polynomials and Least Squares Approximation -- 3.1.10 Example -- 3.1.11 Theorem -- 3.1.12 Example -- 4 Integral Equations -- 4.1 Introduction -- 4.1.1 Definition-Integral Equation -- 4.1.2 Example -- 4.1.3 Definition-First Type Integral Equation -- 4.1.4 Definition-Kernel -- 4.1.5 Definition-Homogeneous Integral Equation of the Second Type -- 4.1.6 Definition-Volterra Integral Equation -- 4.1.7 Definition-Integro-Differential Equation -- 4.1.8 Definition-The Integro-Differential Equation -- 4.1.9 The Relationship Between Integral Equations and Differential Equations -- 4.1.10 Lemma -- 4.1.11 Lemma -- 4.1.12 Lemma -- 4.1.13 Definition -- 4.2 Continuous Functions x(.) and L2 -- 4.2.1 Definition -- 4.2.2 Definition -- 4.2.3 Definition. ; 4.2.4 Definition -- 4.2.5 Cauchy-Schwarz Inequality Theorem -- 4.2.6 Theorem -- 4.2.7 Definition-Continuous Norm of a Continuous Kernel -- 4.2.8 Definition-Linear Operator -- 4.3 Production of Two Kernels -- 4.3.1 Lemma -- 4.3.2 Remark -- 4.3.3 Lemma -- 4.3.4 Definition -- 4.3.5 Fubini Theorem -- 4.3.6 Tonley-Hopson Theorem -- 4.3.7 Lemma -- 4.4 Fredholm Integral Equation of the Second Type -- 4.4.1 Definition-Regular Value -- 4.4.2 Theorem -- 4.4.3 Theorem -- 4.5 Continuous Kernels -- 4.5.1 Theorem -- 4.6 Adjoint Kernels -- 4.6.1 Definition -- 4.6.2 The Combination of Two Adjoint Functions -- 4.6.3 Definition-Normal Kernel -- 4.6.4 Remark -- 4.6.5 Adjoint Equations -- 4.6.6 Definition -- 4.6.7 Lemma -- 4.6.8 Remark -- 4.6.9 Theorem -- 4.6.10 Theorem -- 4.6.11 Example -- 4.6.12 Definition -- 4.6.13 Definition-Point Wise Convergence -- 4.6.14 Definition-Uniformly Convergence -- 4.6.15 Example -- 4.6.16 Definition -- 4.6.17 Definition -- 4.6.18 Definition -- 4.6.19 Theorem -- 4.6.20 Theorem -- 4.6.21 Theorem -- 4.6.22 Theorem -- 4.6.23 Theorem -- 4.6.24 Theorem -- 4.6.25 Theorem -- 5 Numerical Solution of Integral Equations -- 5.1 Introduction -- 5.2 Neumann Series -- 5.2.1 Theorem -- 5.2.2 Example -- 5.2.3 Error Calculation -- 5.3 Nystrom Method -- 5.3.1 Theorem -- 5.4 Gauss-Chebyshev Method -- 5.4.1 Chebyshev Expansion -- 5.4.2 Closed Gauss-Chebyshev Rule -- 5.4.3 Theorem -- 5.4.4 Disadvantages of the Gauss-Chebyshev Method -- 5.5 Non-singular Functions -- 5.5.1 Definition -- 5.5.2 Definition -- 5.5.3 Example -- 5.5.4 Example -- 5.5.5 Example -- 5.5.6 Example -- 5.6 Expansion Method -- 5.7 Collocation Methods -- 5.7.1 Example -- 5.8 Norm Chebyshev -- 5.9 Least Squares Method (L2-Norm Method) -- 5.9.1 Example -- 5.10 Numerical Solution of the Second Kind Integral Equations -- 6 Numerical Methods for Integral-Differential Equations -- 6.1 Introduction. ; 6.2 Integral-Differential Equations -- 6.2.1 Example -- 6.3 El-Gendi Method -- 6.3.1 Example -- 6.4 Fast Galerkin Method -- 7 Introduction to Interval Integral Equations -- 7.1 Introduction -- 7.2 Interval Fredholm Integral Equations -- 7.2.1 Definition-Dual Interval System -- 7.2.2 Definition -- 7.2.3 Theorem -- 7.2.4 Remark -- 7.2.5 Definition: The Interval Number Vector -- 7.2.6 Definition -- 7.2.7 Definition -- 7.3 Interval Fredholm Integral Equation -- 7.3.1 Residual Minimization Method -- References.
• Titolo autorizzato: A Course on Integral Equations with Numerical Analysis
• ISBN: 3-030-85350-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910522937903321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematical engineering.