2D PDE Solver using Finite Difference -- 2

₹600-1500 INR

Closed

Posted 4 months ago

₹600-1500 INR

Paid on delivery

I need a numerical solution for a 2D partial differential equation (PDE) using the Finite Difference Method (FDM). Key Requirements: - Discretize the given PDE in space to create a large system of ordinary differential equations (ODEs). - Employ implicit time integration and Newton's method to find stable, time-dependent solutions. - Ensure computational stability and accuracy throughout the process. Ideal Skills and Experience: - Strong background in numerical methods for PDEs, specifically using FDM. - Proficiency in solving large ODE systems. - Experience with implicit time integration techniques. - Familiarity with Newton's method for iterative solution processes. - Ability to work with 2D PDE systems and ensure stability in computations. Please provide a brief overview of your relevant experience and ensure you meet the technical requirements.

Python

C++ Programming

Simulation

Engineering Mathematics

Matlab and Mathematica

Mathematics

Engineering

Algorithm

Project ID: 40182952

About the project

5 proposals

Remote project

Active 2 mos ago

Looking to make some money?

Email address

Benefits of bidding on Freelancer

Set your budget and timeframe

Get paid for your work

Outline your proposal

It's free to sign up and bid on jobs

5 freelancers are bidding on average ₹1,090 INR for this job

@syedfahadahmad33

Hello I just read out your description and am interested in your project. I am an Expert in FDM And also did in the past. If you need Quality Work, then feel free to contact me Thanks

₹1,050 INR in 7 days

3.8

(2 reviews)

3.1

@rajahunainweb

Hi there, I understand you are seeking a numerical solution for a 2D partial differential equation (PDE) using the Finite Difference Method (FDM). I can help you discretize the PDE in space, create an extensive system of ordinary differential equations (ODEs), and implement implicit time integration alongside Newton's method to achieve stable, time-dependent solutions. With over 3 years of experience in numerical methods and a strong background in Python, Matlab and Mathematica, and algorithm development, I specialize in tackling complex engineering challenges. I have a proven track record in solving large systems of ODEs while ensuring computational stability and accuracy. You can find my portfolios here: https://www.freelancer.com/u/rajahunainweb I look forward to the opportunity to collaborate on this project. Thank you, Regards, Raja Hunain

₹1,050 INR in 7 days

0.0

(0 reviews)

0.0

@SdeShahid

Hi, I have worked with Numerical Methods and familiar with 2D partial differential equation using FDM, lets connect to discuss the solution for you!

₹1,050 INR in 1 day

0.0

(0 reviews)

0.0

@karthikBaskar06

Hi there, I am a cs undergrad with a strong background in Numerical Analysis and Python Simulation. I understand you need a stable solver for a 2D PDE using Finite Difference Methods (FDM). Since you require Newton’s Method and implicit time integration bcz of that reason I will assume you are dealing with a non-linear system (likely a reaction-diffusion or transport problem). My Approach: -> Discretization: I will map your 2D domain into a sparse matrix system using Python (NumPy/SciPy). -> Solver Logic: I will implement the Newton-Raphson loop to ensure convergence at every time step, ensuring the "stability" you asked for. -> Visualization: I'll include a Matplotlib heat map so you can see the solution evolve over time. I have the core boilerplate code ready and can adapt it to your specific equation immediately. Best, Karthik

₹1,250 INR in 1 day

0.0

(0 reviews)

0.0

@CauaAlves

Hello! I'm a Python numerical analyst with expertise in finite difference methods for 2D PDEs, building stable solvers with spatial discretization to large ODE systems, implicit time-stepping, and Newton's method for nonlinear solves. Understanding your needs: Discretize a 2D PDE spatially (e.g., central differences on grid), create ODE system, use implicit integration (backward Euler/Crank-Nicolson), implement Newton iterations with Jacobian for accuracy/stability. My plan: Discuss exact PDE, domain, boundary/initial conditions. Implement grid setup and finite difference stencils (sparse matrices via scipy). Time marching: Implicit scheme with Newton solver (analytic/custom Jacobian). Features: Error handling, convergence checks, visualization (contour/animation with matplotlib). Testing: Validate on benchmark cases, ensure computational efficiency. Deliver: Clean, commented code (script/notebook), README, and sample runs.

₹1,050 INR in 6 days