Calculus of approximations

Consider the equation of heat transfer today.

So that we can find its solution,

We need a grid of points and it will be okay,

And these ideas make an important contribution.

 

Approximations calculus, approximations calculus

Can compute with any precision.

And it will allow us, and it will allow us

To make the right decision.

 

In order to construct a finite difference scheme,

You must replace a derivative by divided difference.

And you may use the balance method, which is mainstream,

To check the property of conservativeness.

 

Use the finite differences, use the finite differences

Choosing some proper stencil.

But you need to analyse, but you need to analyse

Convergence of your finite difference method.

 

Implicit and explicit methods may have a place,

Implicit methods are usually rather stable.

But you must check the order of accuracy,

Then you will manage to solve the problem, you will be able.

 

Approximations calculus, approximations calculus

Will help to solve a linear system

But it requires time for us, but it requires time for us

To obtain an accurate approximation.