Description
Return right-to-left finite-difference spacing ratio.
A truncation term and a rigorous error bound require different information. Taylor and quadrature bounds need derivative bounds over the entire relevant interval; a derivative sampled at one point or a leading asymptotic term does not automatically control the full approximation error.
Return right-to-left finite-difference spacing ratio.
When to use this tool
Use Finite Difference Node Spacing Ratio when checking the stated approximation term or derivative-bound calculation.
How to use the tool and how it works
- Enter left, center, right. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio, symmetric. Inspect symmetric before interpreting the associated values.
Return right-to-left finite-difference spacing ratio. Require left < center < right; ratio = (right-center)/(center-left), symmetric uses exact spacing equality.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number. |
| center | Center | Required. Finite number. |
| right | Right | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Ratio | Required. Finite number. |
| symmetric | Symmetric | Required. Boolean. |
{
"input": {
"left": 0,
"center": 1,
"right": 3
},
"output": {
"ratio": 2,
"symmetric": false
}
}Limitations and assumptions
- No derivative stencil, node uncertainty or convergence guarantee is computed; equality has no tolerance.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Establish the required smoothness and interval-wide bounds for a rigorous estimate; analyze the complete numerical approximation when only local derivative data are available.
References
Similar or alternative tools
- Calculus: Scalar Central Difference Error Term
Return the leading central-difference derivative error term.
- Midpoint Rule Supplied Curvature Bound
Return a composite-midpoint quadrature error bound.