Your terminology is wrong.There is not such a process as Mathematical Simulation.The correct is Mathematical Modelling and (computer ) Simulation.

A mathematical model is a description of a system using mathematics and mathematical concepts (often pde's).

(Computer)Simulation is the simulation run (on computers) to reproduce the behaviour of a system (that has been modelled as above).

A computer model refers to the algorithms and equations describing the modelled system.Simulation refers to the actual running of the program that contains these algoriths and equations

Janamejay,

having studied over the years several dozends of mathematical and physical problems by simulation, I could tell a lot about these matters. However, your careless unspecific question does not invite to do so.

I always thought engineers used this term to mean they were simulating intelligent thinking by replacing it by mindless calculations.

@ulrich

i agree with you that my question is careless and unspecific . After that this is not a answer of my question.

In engineering it is most often the simulation of the evolution of a physical system over time, by solving one or a group of mathematical equations that model the physical system. I agree that your question is too general to merit a specific answer. Try asking how a particular physical problem is modeled and how those models are subsequently solved.

For example in fluid dynamics (you tagged CFD), the Navier-Stokes equations are equations of motion that can accurately describe many aspects of fluid behavior, but are extremely challenging to solve either by hand or on a computer. Especially in the presence of turbulence which develops on a huge range of time and length scales.

For me mathematical simulation is the time saving technique to solve complex problems (many variables, many steps...). Just remember the Nobel prizes in chemistry just now. Mathematical simulation is possible if you know exactly the laws of the process in question and then you are successful to develop a mathematical formalism. The results have to be checked.

Janamejay,

you did not get my point. My intent was not to answer your question but to invite you to reformulate your question in a way that answering it makes sense.

Briefly, when you consider the performance or behavior of phenomena or some thing theoretically, it could be the mathematical simulation.

a very simple answer I want to give; that is: Mathematical simulation is an process to identify and predict the behavior ,performance and optimization of some physical or abstract systems corresponding to various scientific and engineering applications.

It is not easy to give a useful answer in this thread because the original question is a bit too general.

One very interesting use of simulation is the following case. Suppose we have some observed/measured data that represent the contribution of several effects (say, A, B, C) which cannot be separated experimentally. If we are interested solely in one of the effect, (say, A) and if the undesirable effects (B and C) are accessible to simulation, then their contribution can be estimated and subtracted out.

Your terminology is wrong.There is not such a process as Mathematical Simulation.The correct is Mathematical Modelling and (computer ) Simulation.

A mathematical model is a description of a system using mathematics and mathematical concepts (often pde's).

(Computer)Simulation is the simulation run (on computers) to reproduce the behaviour of a system (that has been modelled as above).

A computer model refers to the algorithms and equations describing the modelled system.Simulation refers to the actual running of the program that contains these algoriths and equations

Dear N.C.Markatos,

You are right with Your critics of the terminology, but for me I understood the question immediatly. For me mathematical simulation is the same as simulation of processes using mathematical methods. So what is the benefit to disuss about terminology?

Simply economy of thought!

Dear HANNO,

YOU understood! How about the others? Rigour in terminology assists communication and saves time.

NM

Dear NM, I never tried to save time when thinking. I prefer to open my mind and play around. There is a great difference to my teaching work. There I consist on logical treatment and presentation.

Kind regards

Hanno

Dear HK , when thinking no, but when reading all the above?

Best Regards

Nikos

Dear NC, I like to learn, to see different meanings andI l lilke amusement.

Greetings

HK