Dear Debabrata Biswas,

If you are interested in the solution of PDEs then I may recommend to use MatLab or Mathematica. If you are interested in research and new methods I suggest you to study spectral methods. You may start by solving a simple PDE and use different kinds of wavelets and orthogonal polynomials to approximate the solution of PDEs. I think you may show the equation such that we can send you the appropriate commonds.Thanks

Dear Debabrata,

I suggest you to use freefem++. It is a good softwar which use finite elements method to resolve a PDE. You have only to give it the weak formulation of its equation and you get the solution.

If you want to write a program by yourself, I suggest  you to use finite difference method because the programming of this method is easy.

Dear Debabrata Biswas,

If you are interested in the exact solution of PDEs then I may recommend to use  Mathematica or Maple. If you are interested in the numerical  solution of PDEs, you could try MATLAB.

Thanks

Thanks Dr. H. Khalil, Dr. H. Khalil and Dr. G. W. Wang for your valuable suggestions.

I am familiar with the fact that, PDE can have analytical solution in MATLAB, MATHEMATICA or MAPLE. My main concern is to solve it numerically. I have installed FreeFem++-3.32-1 in my Ubuntu environment. I found it is quite fine for this purpose. Till now I don't know any thing about the programming in this software. My first concern is to solve the Schrodinger equation with harmonic potential,

$$i\hbar\frac{\partial{\Psi(x,t)}}{\partial{t}}=-\frac{hbar ^2}{2m}\frac{\partial^2{\Psi(x,t)}}{\partial{x^2}}+(1/2)m\omega^2 x^2\Psi(x,t)$$.

Can any body suggest the programming for this equation in FreeFem++.

Thank You.

I think MATLAB may be the best choice

The most easiest one in COMSOL. Almost all of single and system of PDEs could be solved with COMSOL

Mathematica uses the "Method of lines" but for certain types of PDE only. This is an interesting project for writing your own program. It can be used to try to solve Uxx+Uyy=0; U(0,y)=0; U(1,y)=0,U(x,0)=0 U(x,1)=sin2PIx for instance.

Hi Debabrata Biswas,

You may want to check out another finite element program called FEniCS. This is a parallel project to FreeFem++. Someone even seems to work on the Schroedinger equation in 2D. Here a link

http://fenicsproject.org/qa/3215/solving-2d-schrodinger-equation

I found FEniCS has a good interface and a problem is easily defined and solved, whilst its bilinear forms can be built from already implemented smaller bilinear forms (e.g. (Grad u, Grad v) and loads more).

Whatever you use. Good luck.

I use Iterative Differential Quadrature Method(IDQM) to  solve PDE with boundary condition in MATLAB. Evey kind of PDE can be solved numerically and easily.

Initial Value Problems (IVPs)  can be solved easily but Boundary value Problems (BVPs) are able to solved IDQM. If you send me your problem, I can give you the required results.

Also the above method solve nonlinear PDE numerically.

Let's send me your problem

Assdociate Prof.Dr. Zekeriya Girgin

Mostle we use mathematica for the solution of PDE's

If you are interested in numerically solving this kind of PDE,

a possible approach consists in the use of Finite Diference Schemes. In this case,

you may translate the  mathematical model  of the problem in some high level programming language.  Among others, Matlab is a programming tool to achieve this purpose.

From my understanding of Partial Differential Equations (PDEs), there there are certain steps along the solution processes that are not understood by softwares. Hence, makes it very difficult and sometimes impossible to get to the desired solutions to its conclusion. But I think Maple is the best software. you can try using the command 'pdsolve'.

if you are interested to find the analytical solutions of PDE, then you can easily apply the Maple or Mathematica software.

I think Octave is the best (its Free), but if you are interested to find analytical solutions, you can use Maple.

For Octave see: http://waxworksmath.com/Software/pdeone_rkc.html

Maple is suitable for your work. 

Hello Debabrata Biswas 

The best numerical method for solving PDEs is the finite element method that can handle irregular meshes, nonlinear equations (by iteration) and is easily automated. When the mesh is uniform the finite difference method is preferred by some researchers because it is easier to understand and also it yields a system of algebraic equations of smaller number of unknowns. 

Hello, 

I recommend you COMSOL. The specific module for PDEs make the COMSOL very comfortable to work with. You can find how to work with COMSOL with some Videos from COMSOL company and some other in YouTube. However, this software is not free. You need to learn how to introduce your own equation and sign different boundary condition. 

It all depends on your choice. MATLAB, Mathematical, COSMOL, Maple, etc can do it for you. Pick the language you like among these and work around it. Cheers. BUT I use MATLAB most times.

I have used several times mathematica 9  software  for ODE's and PDE's 

In my opinion, Matlab maybe one of the best choice.

Hello, I've just started working on this, and while many of the suggestions are very good, they're all proprietary software solutions.

I've found an example of a software that solves PDE's in 2D mesh arrays:

https://people.sc.fsu.edu/~jburkardt/f77_src/toms565/toms565.html

It's called PDETWO, it's quite old but, to my knowledge, it's one of the best (open source) pde solver out there. It uses the method of lines to discretize the space variables and generate an approximate ODE system.

There's also TWODEPEP, which is also 2D and solves elliptic, parabolic and eigenvalue pde's, this one uses the finite element method to solve the pde's.

I know it is an old question, but I hope this helps.

https://www.scopus.com/record/display.uri?eid=2-s2.0-0020113492&origin=inward&txGid=BD4736B30D0AAD72BC9CBB47D96D35E9.wsnAw8kcdt7IPYLO0V48gA%3a2

https://people.sc.fsu.edu/~jburkardt/f77_src/toms565/toms565.html

Thanks a ton

Well, I have two options to suggest. MATLAB is very good and with almost limitless functions/toolboxes but not free. Python is another choice , not too many toolboxes in python but it's free.

 Hello sir,

Actually, to have a precise suggestion, it may depend on the project you are working on. But MATLAB would be a beneficial choice, as I found in my own project.

Moreover, if it is any help, finite difference method would be a good choice and simple procedure to investigate spatiotemporal patterns, which are based on time and spatial variables, both together.

I personally use Matlab Codes to solve linear or nonlinear time dependent partial differential equations in one or two dimensional spaces.

I would say Matlab for sure!

matlab or mathematica

Can anyone help me on PDEs modelling plz??

what kind of PDE are you modeling ?

Matlab is very good method

matlab

There are Fortran codes in the TOMS library, found for example at netlib.org, which may solve this problem. PDEs may need special handling, based on their characteristics - for example, the PDEs found in incompressible CFD cannot be solved by the standard libraries and need special handling (which brings in the SIMPLE algorithm) to handle some of the degenerate aspects of the equations.

MATLAB has an add-on library for PDEs, which may be useful - I have not used it. If Matlab has such a library then check to see if Octave has an equivalent, or (a little less likely) Scilab.

I've seen that Julia is targeting the field of differential equations, so may be worth a look - I've never programmed in Julia, but noticed this week that they have a large GPU-enabled library for ODEs.

I think it would help to show the PDE you are trying to solve. Secondly, do you require analytical or numerical solutions?

Hi Debabrata,

You could always use Mathematica/Matlab to solve PDEs, especially if you're looking for analytical solutions. In case you're looking for a numerical solution and are comfortable enough with Finite Element ANalysis, enough to formulate the weak form of your PDE, you could try using FEniCS (https://fenicsproject.org).

Hope this helps!

Matlab is a flexible tool that can be useful in handling the three major types of PDEs.

Hi. I would recomand Freefem. You can solve PDEs in Finite Element and its a open source program.

Freefem++ and MatLab.

free PDE solvers with phase-field capabilties

https://pages.nist.gov/pfhub/codes/

Mathematica - Wolfran

Hi. You can use Matlab and FEniCS project to solve PDEs. There are some PDEs which are already solved which you can see in its demos.

Other very good software based on finite elements is COMSOL.

However it is paid. It generates excellent visual results.

You can use pdepe function of Matlab

If the magnetic field is continuous and occupies all the space, how can I explain to my students why there are only a few lines of magnetic field in the famous experiment with iron filings?

Hello dear Debabrata Biswas

To solve the Partial Differential Equations you can use MATLAB which has a special toolbox for PDF(Partial Differential Equations), but if you not familiar with that and want to solve your problem manually, I'm sharing some MATLAB files(.m) with you, you can use to solve with the help of them, note that MATLAB has more accuracy than the other softwares.

Thank you so much!

Muhammad Sinan

If you want EXACT solutions to constant-coefficients linear second-order partial differential equations (heat, wave and Laplace equations, say) under very general boundary conditions, obtained by Fourier methods, you can try our Maxima's package "pdefourier". You can see some examples here: https://github.com/emmanuelroque/pdefourier and there is an accompanying paper: Preprint Automated solving of constant-coefficients second-order line...

you can also try in COMSOL, it is also a good tool to simulate the PDE. There is a special module called Mathematics Modul to solve a PDE and simulate a different kinds of equation-based modeling.

go for MATLAB / Mathematical

Kindly find a detailed comparison in the following link: https://www.stochasticlifestyle.com/comparison-differential-equation-solver-suites-matlab-r-julia-python-c-fortran/ Debabrata Biswas

go for matlab or mathematica

Many software can do it for you. I prefer Maple for PDEs. Mathematica also works, but seems less powerful than Maple for PDEs

If you are looking for an analytical solution for a partial differential equation I recommend Mathematica, the latest version is very powerful in the calculating of the solutions, see the link ( https://reference.wolfram.com/language/howto/SolveAPartialDifferentialEquation.html), if you are looking for a numerical solution I think it's better to use MATLAB, so it depends on what you need.

In general, if you are not familiar with the programming language, you'd better use Mathematica, it's easier.

Best regards,

Dans Matlab il y a une bibliothèque pour la résolution des pde numériquement

Python with pytorch package

The type of PDE you want to solve has to be identified, it also may determine the algorithm to be applied. The PDE may be an IVP, a BVP or an IBVP. This need be specified first.

Most books and articles (papers) are using Matlab. There are other softwares such as Maple, Mathematica, Python.....

Concerning the numerical algorithms/ Methods: FDM, FEM, BEM....can be used for BVPs based on the domain type. There are also numerical methods for IVPs.

Thanks!

Different types of PDEs may need different or the same software.

Your PDE may be linear or nonlinear IVP or BVP, quasi-linear BVP...

FEM, FDM, FVM, BEM... may be used based on the domain and PDE type.

Matlab, Maple,....can be used.

There also different FEM-softwares....

Thanks!

Maple

Matlab is best software.

It depends on your programming skills.

- If you have prior knowledge of python then better to choose Fenics. It’s very popular in scientific computing areas.

- If you have prior knowledge of c or c++ then go for freeFem++. It’s really very fast.

- If you have prior knowledge of Matlab then better to choose Matlab. Matlab is slow compared to freeFem++.

- If you don’t want to learn any programming language then better to choose Comsol, but it is not free.

Note: Matlab and Comsol are most user friendly softwares in this fields.

Thank you.

https://www.researchgate.net/post/Which_one_do_you_prefer_for_statistics_and_Econometrics_Eviews_or_Spss_or_Stata_Matlab_or_R_or_Python_why

I think so COMSOL . It have own equation building.

https://arxiv.org/pdf/2308.01245.pdf

https://visualpde.com/