Numerical Differentiation Numerical Differentiation Finite Difference Numerical Differentiation

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Numerical Differentiation •

Numerical Differentiation •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

Truncation Error Analysis: First Derivative •

Truncation Error Analysis: First Derivative •

Truncation Error Analysis: First Derivative •

Truncation Error Analysis: First Derivative •

Truncation Error Analysis: Second Derivative •

Truncation Error Analysis: Second Derivative •

Truncation Error Analysis: Non-Uniform Grid •

Truncation Error Analysis: Non-Uniform Grid •

Numerical Differentiation: Finite Difference •

Numerical Differentiation: Finite Difference •

General Technique for Construction of Finite Difference Scheme of Arbitrary Order • Method of

General Technique for Construction of Finite Difference Scheme of Arbitrary Order • Method of Undetermined Coefficients

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example •

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example •

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example •

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example •

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example •

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example •

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example • LHS

General Technique for Construction of Finite Difference Scheme of Arbitrary Order: Example • LHS RHS RHS

Forward Finite Difference Schemes of Arbitrary Orders

Forward Finite Difference Schemes of Arbitrary Orders

Backward Finite Difference Schemes of Arbitrary Orders

Backward Finite Difference Schemes of Arbitrary Orders

Central Finite Difference Schemes of Arbitrary Orders

Central Finite Difference Schemes of Arbitrary Orders

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation • Combine terms to result in derivative estimates of TE O(h 2)

Richardson’s Extrapolation • Combine terms to result in derivative estimates of TE O(h 2)

Richardson’s Extrapolation • Combine terms to result in derivative estimates of TE O(h 3)

Richardson’s Extrapolation • Combine terms to result in derivative estimates of TE O(h 3)

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Richardson’s Extrapolation •

Partial Derivatives •

Partial Derivatives •

Partial Derivatives •

Partial Derivatives •

Tutorial 10 Problem 2 Sol:

Tutorial 10 Problem 2 Sol:

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