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References

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Differentiation - Method Based on Finite Difference

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By backward difference

\frac{dy}{dx}

is given by

a:

\frac{y_{i-1} + y_i}{h}

Explanation

Explanation

b:

\frac{y_i - y_{i-1}}{h}

Explanation

Explanation

c:

\frac{y_i + y_{i-1}}{h}

Explanation

Explanation

d:

\frac{y_{i-1} - y_i}{h}

Explanation

Explanation

By forward difference

\frac{dy}{dx}

is given by

a:

\frac{y_{i+1} - y_i}{h}

Explanation

Explanation

b:

\frac{y_i + y_{i+1}}{h}

Explanation

Explanation

c:

\frac{y_i - y_{i+1}}{h}

Explanation

Explanation

d:

\frac{y_{i+1} + y_i}{h}

Explanation

Explanation

By central difference

\frac{dy}{dx}

is given by

a:

\frac{y_{i-1} + y_{i+1}}{h}

Explanation

Explanation

b:

\frac{y_{i+1} + y_{i-1}}{h}

Explanation

Explanation

c:

\frac{y_{i-1} - y_{i+1}}{h}

Explanation

Explanation

d:

\frac{y_{i+1} - y_{i-1}}{h}

Explanation

Explanation

\frac{d^2y}{dx^2}

is given by

a:

\frac{y_{i+1} - y_i + y_{i-1}}{h^2}

Explanation

Explanation

b:

\frac{y_{i+1} + 2y_i - y_{i-1}}{h^2}

Explanation

Explanation

c:

\frac{y_{i+1} - 2y_i + y_{i-1}}{h^2}

Explanation

Explanation

d:

\frac{y_{i+1} + y_i - y_{i-1}}{h^2}

Explanation

Explanation

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