IGNOU BMTE 144 2026 - If , find the values of C1 and C2.

Question

If $\delta^2 f(x_0) = C_1 h^2 f''(x_0) + C_2 h^4 f^{(4)}(x_0) + \dots$ , find the values of C₁ and C₂.

09 Jan 2026

Answer :

Word Count : 199

Given the finite difference approximation for the second difference: [ \delta^2 f(x_0) = C_1 h^2 f''(x_0) + C_2 h^4 f^{(4)}(x_0) + \cdots ] We want to find constants (C_1) and (C_2). --- Start with the definition of the second finite difference operator: [ \delta^2 f(x_0) = f(x_0 + h) - 2f(x_0) + f(x_0 - h) ] Use Taylor series expansions

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