by the central difference

USAGE SUMMARY

The phrase "by the central difference" is correct and usable in written English.
It can be used in mathematical or scientific contexts, particularly when discussing numerical methods or approximations. Example: "The derivative can be approximated by the central difference method to improve accuracy."

✓ Grammatically correct

Science

Engineering

Human-verified examples from authoritative sources

Exact Expressions

12 human-written examples

In the chosen method the equations of motion are solved by the central difference scheme.

Engineering Structures

Noise is severely amplified by the central difference, and hence limits the damage identification through the use of modal curvature estimation.

Composite Structures

From the obtained mode shapes, the CMD were calculated by the central difference operation to identify the damage in composite beams.

Composite Structures

The dispersion part is solved by the central difference method and the propagation part is solved implicitly by using the Gauss Seidel iteration method.

Applied Mathematical Modelling

The spatial and temporal derivatives in this method are discretized by the central difference technique and Newmark-Beta algorithm, respectively, and the derivation results in the calculation of a banded-sparse matrix equation.

Journal of Computational Physics

The Extended High-order Sandwich Panel Theory (EHSAPT -based finitEHSAPT -basedused to finiteatelementquatisns of motion, and the time response is obtained by the central difference method.

International Journal of Solids and Structures

Human-verified similar examples from authoritative sources

Similar Expressions

48 human-written examples

The continuous time finite element equations are then integrated in time by using the central difference algorithm.

Journal of Sound and Vibration

The resolution is easily performed with a step-by-step solution technique using the central difference scheme to solve the coupled equation system.

Journal of Sound and Vibration

It, indeed, comes from the truncation error of the central difference scheme used by them.

Journal of Computational Physics

In the Lax or Lax Friedrichs scheme (Lax 1954), the central difference scheme is stabilized by replacing the (Q_{i}^{n}) term with the average (0.5left( {Q_{i + 1}^{n} + Q_{i - 1}^{n} } right)) term in the discretization.

Petroleum Science

However, its application is limited by the requirement for high spatial resolution and reference mode shapes, and the central difference method induced low anti-noise ability.

Measurement

Expert writing Tips

Best practice

When describing numerical methods, specify the order of the central difference scheme (e.g., second-order central difference) for clarity.

Common error

Avoid using "by the central difference" when a different numerical method is actually being used. Ensure that the described method truly involves a central difference approximation.

Linguistic Context

The phrase "by the central difference" functions primarily as a prepositional phrase modifying a verb, often indicating the method or means by which a calculation or approximation is performed. Ludwig provides examples of its usage in scientific contexts.

Expression frequency: Uncommon

Frequent in

Science

80%

Engineering

10%

Formal & Business

5%

Less common in

News & Media

3%

Academia

1%

Reference

1%

Ludwig's WRAP-UP

In summary, the phrase "by the central difference" is a technical term primarily used within scientific and engineering disciplines. As Ludwig AI indicates, it correctly describes the application of a specific numerical method for approximation, particularly in solving differential equations or estimating derivatives. While grammatically sound, it is most appropriate for formal and scientific contexts due to its specialized nature. For more general audiences, simpler alternatives might be preferred. Common related phrases include "using the central difference method" and "via central difference approximation". When using the phrase, ensure clarity by specifying the order of the scheme and avoid confusing it with other numerical methods.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

using the central difference method

Rephrases the action to emphasize the method's application.

via central difference approximation

Specifies the technique as an approximation, highlighting a particular type of numerical method.

applying the central difference scheme

Focuses on the 'scheme' aspect, useful when discussing algorithms or computational structures.

employing the central difference formula

Emphasizes the 'formula' aspect, suitable when referencing specific equations.

utilizing central difference techniques

Highlights the use of multiple central difference approaches.

with the central difference approach

Focuses on conceptual methodology.

through central difference discretization

Highlights the discretization procedure involved.

based on central difference calculations

Focuses on the computational aspect.

determined from the central difference

Highlights the central difference as the determining factor.

computed using central differencing

Emphasizes the computational aspect of the central difference.

FAQs

How can I use "by the central difference" in a sentence?

You can use "by the central difference" to describe a method of approximation, such as, "The derivative was calculated "by the central difference" method".

What are some alternatives to saying "by the central difference"?

Alternatives include "using the central difference method", "via central difference approximation", or "applying the central difference scheme".

In what contexts is "by the central difference" typically used?

The phrase is commonly used in mathematical, scientific, and engineering contexts when describing numerical methods for approximating derivatives or solving differential equations.

Is it appropriate to use "by the central difference" in informal writing?

While grammatically correct, "by the central difference" is highly technical and may not be suitable for informal writing. Simpler explanations are preferable for general audiences.