Question

What does the Taylor series expansion help determine for the finite-difference equation's right-hand side?

a) Truncation error
b) Absolute error
c) Round-off error
d) Precision error

Answer 1

The Taylor series expansion helps determine the truncation error for the finite-difference equation's right-hand side.

Step-by-step explanation:

The Taylor series expansion helps determine the truncation error for the finite-difference equation's right-hand side. Truncation error is the difference between the actual value and the approximate value obtained from a numerical method. The Taylor series expansion approximates a function using a polynomial, and by comparing the approximation with the finite-difference equation's right-hand side, we can estimate the truncation error.

For example, if we have a finite-difference equation that approximates the derivative of a function, the Taylor series expansion can give us an expression for the exact derivative. By subtracting the finite-difference equation's right-hand side from the exact derivative expression, we can determine the truncation error.

Therefore, the correct answer is a) Truncation error.