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Record Nr. |
UNINA9910860865603321 |
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Autore |
Dukkipati R.V |
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Titolo |
Applied Numerical Methods Using MATLAB |
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Pubbl/distr/stampa |
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Bloomfield : , : Mercury Learning & Information, , 2023 |
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©2023 |
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ISBN |
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9781683928676 |
9781683928683 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (1225 pages) |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Cover -- Half-Title -- Title -- Copyright -- Contents -- Preface -- Chapter 1: Numerical Computations -- 1.1 Taylor's Theorem -- 1.2 Number Representation -- 1.3 Error Considerations -- 1.3.1 Absolute and Relative Errors -- 1.3.2 Inherent Errors -- 1.3.3 Round-off Errors -- 1.3.4 Truncation Errors -- 1.3.5 Machine Epsilon -- 1.3.6 Error Propagation -- 1.4 Error Estimation -- 1.5 General Error Formula -- 1.5.1 Function Approximation -- 1.5.2 Stability and Condition -- 1.5.3 Uncertainty in Data or Noise -- 1.6 Sequences -- 1.6.1 Linear Convergence -- 1.6.2 Quadratic Convergence -- 1.6.3 Aitken's Acceleration Formula -- 1.7 Summary -- Exercises -- Chapter 2: Linear System of Equations -- 2.1 Introduction -- 2.2 Methods of Solution -- 2.3 The Inverse of a Matrix -- 2.4 Matrix Inversion Method -- 2.4.1 Augmented Matrix -- 2.5 Gauss Elimination Method -- 2.5.1 MATLAB Program for the Gauss Elimination Method -- 2.6 Gauss-Jordan Method -- 2.6.1 MATLAB Program for the Gauss Jordan Method -- 2.7 Cholesky's Triangularization Method -- 2.8 Crout's Method -- 2.8.1 MATLAB Program for Crout's Method -- 2.9 Thomas Algorithm for Tridiagonal System -- 2.9.1 MATLAB Program for the Thomas Method for Tridiagonal Systems -- 2.10 Jacobi's Iteration Method -- 2.10.1 MATLAB Program for the Jacobi Iteration Method -- 2.11 Gauss-Seidel Iteration Method -- 2.11.1 MATLAB Program for the Gauss Seidel Method -- 2.12 Symmetric Matrix Eigenvalue Problems -- 2.12.1 The |
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Jacobi Method -- 2.12.2 MATLAB Function for the Jacobi Method -- 2.12.3 Householder Reduction to Tridiagonal Form -- 2.12.4 Gerschgorin's Circle Theorem -- 2.12.5 Sturm Sequence -- 2.12.6 QR Method -- 2.12.7 Power Method -- 2.12.8 Inverse Power Method -- 2.13 Summary -- Exercises -- Chapter 3: Solution of Algebraic and Transcendental Equations -- 3.1 Introduction -- 3.2 Bisection Method -- 3.2.1 Error Bounds. |
3.3 Method of False Position -- 3.3.1 MATLAB Program for the False Position Method -- 3.4 Newton-Raphson Method -- 3.4.1 Convergence of the Newton-Raphson Method -- 3.4.2 Rate of Convergence of the Newton-Raphson Method -- 3.4.3 MATLAB Program for the Newton Raphson Method -- 3.4.4 Modified Newton-Raphson Method -- 3.4.5 Rate of Convergence of Modified Newton-Raphson Method -- 3.5 Successive Approximation Method -- 3.5.1 Error Estimate in the Successive Approximation Method -- 3.6 Secant Method -- 3.6.1 Convergence of the Secant Method -- 3.6.2 MATLAB Program to Search for a Root of the Function f(x) in the Interval (a,b) -- 3.6.3 MATLAB Program for Secant Method -- 3.7 Muller's Method -- 3.7.1 MATLAB Program for Muller's Method -- 3.8 Chebyshev Method -- 3.9 Aitken's Δ2 Method -- 3.10 Brent's Method -- 3.10.1 MATLAB Program for Brent's Method -- 3.11 Newton Method for a System of Nonlinear Equations -- 3.12 Comparison of Iterative Methods -- 3.13 MATLAB Built-in Function: fzero -- 3.14 Summary -- Exercises -- Chapter 4: Numerical Differentiation -- 4.1 Introduction -- 4.2 Derivatives Based on Newton's Forward Integration Formula -- 4.2.1 MATLAB Program for Derivatives Based on Newton's Forward Integration Formula-Equally Spaced Points -- 4.3 Derivatives Based on Newton's Backward Interpolation Formula -- 4.4 Derivatives Based on Stirling's Interpolation Formula -- 4.5 Maxima and Minima of a Tabulated Function -- 4.6 Cubic Spline Method -- 4.7 Richardson Extrapolation -- 4.8 Differentiation of Unequally Spaced Data -- 4.9 MATLAB Built-in Functions: diff and gradient -- 4.10 Summary -- Exercises -- Chapter 5: Finite Differences and Interpolation -- 5.1 Introduction -- 5.2 Finite Difference Operators -- 5.2.1 Forward Differences -- 5.2.2 Backward Differences -- 5.2.3 Central Differences -- 5.2.4 Error Propagation in a Difference Table. |
5.2.5 Properties of the Operator Δ -- 5.2.6 Difference Operators -- 5.2.7 Relation Among the Operators -- 5.2.8 Representation of a Polynomial using Factorial Notation -- 5.3 Interpolation with Equal Intervals -- 5.3.1 Missing Values -- 5.3.2 Newton's Binomial Expansion Formula -- 5.3.3 Newton's Forward Interpolation Formula -- 5.3.4 MATLAB M-file: Newtonint -- 5.3.5 Newton's Backward Interpolation Formula -- 5.3.6 Error in the Interpolation Formula -- 5.4 Interpolation with Unequal Intervals -- 5.4.1 Lagrange's Interpolating Polynomial for Equal Intervals -- 5.4.2 function yint = Lagrangeint (x,y,xx) -- 5.4.3 Lagrange's Formula for Unequal Intervals -- 5.4.4 Hermite's Interpolation Formula -- 5.4.5 Inverse Interpolation -- 5.4.6 Lagrange's Formula for Inverse Interpolation -- 5.5 Central Difference Interpolation Formulae -- 5.5.1 Gauss's Forward Interpolation Formula -- 5.5.2 Gauss Backward Interpolation Formula -- 5.5.3 Bessel's Formula -- 5.5.4 Stirling's Formula -- 5.5.5 Laplace-Everett's Formula -- 5.5.6 Selection of an Interpolation Formula -- 5.6 Divided Differences -- 5.6.1 Newton's Divided Difference Interpolation Formula -- 5.7 Cubic Spline Interpolation -- 5.8 Generalized Spline Method -- 5.8.1 Splines -- 5.8.2 Linear Splines -- 5.8.3 Quadratic Splines -- 5.8.4 Cubic Splines -- 5.8.5 End Conditions -- 5.8.6 MATLAB Built-in Function: spline -- 5.8.7 Multidimensional Interpolation -- 5.8.8 MATLAB Built-in Function: interpl -- 5.9 Summary -- Exercises -- |
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Chapter 6: Curve Fitting, Regression, and Correlation -- Approximating Curves -- Linear Regression -- 6.1 Linear Equation -- 6.2 Curve Fitting With a Linear Equation -- 6.3 Criteria for a Best Fit -- 6.4 Linear Least-Squares Regression -- 6.5 Linear Regression Analysis -- 6.5.1 MATLAB built-in function: polyfit -- 6.5.2 MATLAB built-in function: polyval -- 6.6 Interpretation of a and b. |
Assumptions in the Regression Model -- 6.7 Standard Deviation of Random Errors -- 6.8 Coefficient of Determination -- 6.9 Linear Correlation -- Properties of the Linear Correlation Coefficient r -- Explained and Unexplained Variation -- 6.10 Linearization of Nonlinear Relationships -- 6.11 Polynomial Regression -- 6.11.1 Polynomial Fit -- 6.11.2 MATLAB Built-in Functions for Polynomial Fit -- 6.12 Quantification of Error of Linear Regression -- 6.13 Multiple Linear Regression -- 6.14 Weighted Least-Squares Method -- 6.15 Orthogonal Polynomials and Least-Squares Approximation -- 6.16 Least-Squares Method for Continuous Data -- 6.17 Approximation Using Orthogonal Polynomials -- 6.18 Gram-Schmidt Orthogonalization Process -- 6.19 Fitting a Function Having a Specified Power -- 6.20 Fitting a Cubic Spring Model -- 6.21 Additional Example Problems and Solutions -- 6.22 Summary -- Exercises -- Chapter 7: Numerical Integration -- 7.1 Introduction -- 7.1.1 Relative Error -- 7.2 Newton-Cotes Closed Quadrature Formula -- 7.3 Trapezoidal Rule -- 7.3.1 Error Estimate in Trapezoidal Rule -- 7.3.2 MATLAB Functions: trapz and cumtrapz -- 7.4 Simpson's 1/3 Rule -- 7.4.1 Error Estimate in Simpson's 1/3 Rule -- 7.4.2 MATLAB Program for Simpson's Integration: simpsonint -- 7.4.3 MATLAB Built-in Functions: quad and quad1 -- 7.5 Simpson's 3/8 Rule -- 7.6 Boole's and Weddle's Rules -- 7.6.1 Boole's Rule -- 7.6.2 Weddle's Rule -- 7.7 Romberg's Integration -- 7.7.1 Richardson's Extrapolation -- 7.7.2 Romberg Integration Formula -- 7.7.3 MATLAB Program for Romberg Integration: Romberg -- 7.8 Gaussian Quadrature -- 7.8.1 Gaussian Integration Formulas -- 7.8.2 Orthogonal Polynomials -- 7.8.3 Gauss-Lagendre Quadrature -- 7.8.4 Gauss-Chebyshev Quadrature Method -- 7.8.5 Gauss-Laguerre Quadrature -- 7.8.6 Gauss-Hermite Quadrature. |
7.8.7 MATLAB Programs for Gaussian Quadrature: gaussnodes and gaussquad -- 7.9 Double Integration -- 7.9.1 Trapezoidal Method -- 7.9.2 Simpson's 1/3 Rule -- 7.9.3 MATLAB Built-in Function for Double Integration: dblquad -- 7.10 Summary -- Exercises -- Chapter 8: Numerical Solution of Ordinary Differential Equations -- 8.1 Introduction -- 8.2 One-Step Methods or Single-Step Methods -- 8.2.1 Picard's Method of Successive Approximation -- 8.2.2 The Taylor's Series Method -- 8.3 Step-by-Step Methods or Marching Methods -- 8.3.1 Euler's Method -- 8.3.2 MATLAB Program for Euler's Method: euler -- 8.3.3 Modified Euler's Method -- 8.3.4 MATLAB Program for the Modified Euler's Method: modeuler -- 8.3.5 Runge-Kutta Methods -- 8.3.6 Predictor-Corrector Methods -- 8.4 MATLAB Functions for Ordinary Differential Equations: ode45, ode23, ode113, ode15s, ode23s, ode23t, ode23tb -- 8.5 System of First-order Ordinary Differential Equations -- 8.6 Initial Value Problems -- 8.6.1 The Taylor Series Method -- 8.6.2 Picard's Method -- 8.6.3 Second-Order Runge-Kutta Method -- 8.6.4 Fourth-Order Runge-Kutta Method -- 8.6.5 Euler's Formula -- 8.6.6 Modified Euler's Formula -- 8.6.7 Burlirsch-Stoer Method (Mid-Point Method) -- 8.6.8 The Runge-Kutta-Fehlberg Method -- 8.6.9 The Runge-Kutta-Butcher Method -- 8.7 Two-Point Boundary Value Problems -- 8.7.1 Finite Difference Method -- 8.7.2 Second-Order Differential Equations -- 8.7.3 The Shooting Method -- 8.8 Second-Order Initial Value Problem (IVP) -- 8.9 Second-Order Boundary Value Problem (BVP) -- 8.10 MATLAB Built-in Functions -- |
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8.11 Summary -- Exercises -- Chapter 9: Direct Numerical Integration Methods -- 9.1 Introduction -- 9.2 Single Degree of Freedom System -- 9.2.1 Finite Difference Method -- 9.2.2 Central Difference Method -- 9.2.3 The Runge-Kutta Method -- 9.3 Multi-degree of Freedom Systems -- 9.4 Explicit Schemes. |
9.4.1 Central Difference Method. |
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Sommario/riassunto |
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The book is designed to cover all major aspects of applied numerical methods, including numerical computations, solution of algebraic and transcendental equations, finite differences and interpolation, curve fitting, correlation and regression, numerical differentiation and integration, matrices and linear system of equations, numerical solution of ordinary differential equations, and numerical solution of partial differential equations. MATLAB is incorporated throughout the text and most of the problems are executed in MATLAB code. It uses a numerical problem-solving orientation with numerous examples, figures, and end of chapter exercises. Presentations are limited to very basic topics to serve as an introduction to more advanced topics. FEATURES:Integrates MATLAB throughout the textIncludes over 600 fully-solved problems with step-by-step solutionsLimits presentations to basic concepts of solving numerical methods |
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