Numerical Methods Ver 0.1 (Matlab)
1. Mathematical Preliminaries and Error Analysis
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Absolute Value (o)
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Actual Error (o)
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Absolute Error (o)
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Relative Error (o)
2. Solution of Equations in One Variable
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The Bisection Method (o)
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The Fixed-Point Iteration (o)
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The Newton's Method (o)
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The Secant Method (o)
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The Method of False Postion (o)
3. Interpolation and Polynomial Approximation
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Data Approximation and Neville's Method (o)
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Divided Differences (o)
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Hermite Interpolation (progress)
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Romberg Integrationi (o)
4. Numerical Differentiation and Integration
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Three-Point Midpoint Formula
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Three-Point Endpoint Formula
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Five-Point Midpoint Formula
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Five-Point Endpoint Formula
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Composite Simpson's Rule
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Composite Trapezoidal Rule
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Composite Midpoint Rule
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Romberg Integration
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Adaptive Quadrature Method
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Simpson's Double Integral
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Gaussian Double Integral
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Gaussian Triple Integral
5. Initial-Value Problems for Ordinary Differential Equations
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Euler's Method (o)
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Runge Kutta Method (Order Four) (o)
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Runge Kutta Fehlberg Method (progress)
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Adams Fourth Order Predictor Corrector (o)
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Adams Variable Step Size Predictor Corrector
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Runge Kutta Method for Systems of Differential Equations
6. Direct Methods for Solving Linear Systems
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Gaussian Elimination with Backward Substitution
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Gaussian Elimination with Partial Pivoting
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Gaussian Elimination with Scaled Partial Pivoting
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LU Factorization
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LDL^t Factorization
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Crout Factorization for Tridiagonal Linear Systems