1.01

1.20

1.21

1.10

None

3

6

5

7

None

Four

Five

Three

Two

None

Stability

Precision

Uniqueness

Existence

None

They eliminate the need to formulate a differential-equation model

They are applicable only to homogeneous linear ODEs

None

They always provide exact closed-form solutions

They are used only when an exact analytical solution is available

The formula uses only first-order central differences and nothing else whatsoever

The formula uses only third-order central differences and no other orders at all

The formula uses only odd-order central differences and no even-order differences at all

The formula uses even-order central differences like second, fourth, and sixth differences

None

Even-order differences

Zeroth-order differences only

Odd-order differences only

First-order differences only

None

To increase the interval of integration

To accelerate the convergence of a sequence of numerical estimates

To calculate the weight function

To determine the derivative of the integrand of the numerical function

None

A discipline within mathematics and computer science that focuses on creating and analysing numerical methods

The area of mathematics and computer science concerned with creating, analysing, and implementing algorithms for solving problems numerically

None

The branch of mathematics and computer science devoted solely to exact closed-form solutions of algebraic equations

The subfield of computer science that emphasises formal logic and rigorous software verification techniques

It can be formulated only for partial differential equations

It requires the exact solution to be known at every point

It contains no initial information about the dependent variable

None

It consists of a differential equation with only boundary conditions