PDE Discretization & Implicit Solver

₹600-1500 INR

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Posted 1 day ago

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₹600-1500 INR

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I would like to reproduce the workflow laid out by Hacker & Uecker (2009). The project has three key steps: 1. Discretise my time-dependent PDE in space so it becomes a large, stiff ODE system. 2. Advance that system with an implicit time-integration routine. 3. Use Newton iterations at every step to guarantee stable solutions over long time horizons. I will supply the exact PDE and boundary conditions once we start. Finite-difference, finite-volume, or spectral discretisations are all acceptable as long as the stability matches the paper’s results. The final deliverable should include: • Well-commented source code (Python, MATLAB, or a language you propose) • A short write-up or notebook showing that the implementation reproduces the stable time-dependent behaviour highlighted in the reference paper • Clear instructions so I can rerun the simulations on my own machine If you have experience with stiff ODE solvers, implicit schemes, and Newton iterations, I’d love to hear how you would approach this.

Matlab and Mathematica

Python

Algorithm

Mathematics

Project ID: 40185933

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6 freelancers are bidding on average ₹1,075 INR for this job

@khaliduom103

Hi, I am a mathematician and have a lot of experience in solving boundary value problems in PDE. Its better we discuss the project in chat box. thank you

₹1,250 INR in 1 day

4.9

(40 reviews)

6.0

@divyam12345

Dear Sir/Madam, I understand your requirements, and I can help you reproduce the workflow described by Hacker & Uecker (2009). I have experience with spatial discretisation of PDEs, stiff ODE systems, implicit time-integration schemes, and Newton-based solvers, and I’m confident I can implement a stable, well-documented solution that matches the behaviour reported in the paper. Let’s connect in the chatbox to discuss the project further, including the budget and timeline. To know more about my experience, let's talk in a freelancer call, and I can share more details and sample works in the chatbox. I am ready to work with you, please connect in the chatbox for further discussions. Thank You. Dr. Divya.

₹1,500 INR in 2 days

4.9

(13 reviews)

4.5

@tayyabovgu

Hi, I did my PhD in electrical power and energy systems and am working as a postdoc in this area. I am capable of producing the required result. Please let me know further and we will discuss the project more. i have published a number of V2G and EV charging station and integration papers

₹1,050 INR in 7 days

4.9

(4 reviews)

4.1

@sayarsinghseo

As a highly skilled Python programmer with extensive experience in data analysis, your PDE discretization and implicit solving project stands out to me. Although my main area of expertise is not PDEs, I am well-versed with solving complex problems using numerical methods and Python. Additionally, my knowledge in data analysis equips me with the ability to approach your problem with a unique perspective. I am confident that my proficient Python programming skills combined with my background in data analysis will enable me to tackle the challenging steps of discretizing your PDE in space and advancing the resulting ODE system with an implicit time-integration routine elegantly and effectively. While stable solutions over long time horizons have always been prioritized in both Mathematics and SEO (another field I specialize in), I understand the importance of precision and stability in your project. My crisp, well-commented source code will ensure traceability and reproducibility. Additionally, I will provide a comprehensive write-up or notebook not only showcasing the accuracy of our implementation but also detailing how it aligns with Hacker & Uecker's findings. To ensure you can rerun simulations seamlessly, clear instructional materials will accompany the deliverables. Let's leverage my broad skillset to create efficient and effective solutions for your project!

₹1,000 INR in 1 day

5.0

(1 review)

1.1

@ammad1709

Hello, I can reproduce the Hacker & Uecker (2009) workflow end-to-end with a focus on numerical stability and reproducibility. Proposed Approach: Spatial discretisation: Convert the PDE into a stiff ODE system using finite differences or finite volumes (spectral methods if the PDE structure benefits from them). Grid design and boundary handling will be chosen to match the paper’s stability properties. Implicit time integration: Advance the system using proven stiff solvers (e.g. backward Euler, BDF, or implicit Runge–Kutta), selected based on stiffness and long-time behaviour. Newton iterations: Implement a robust Newton or Newton–Krylov method at each time step with proper Jacobian handling and convergence safeguards. Deliverables Clean, well-commented source code (Python or MATLAB). A short technical write-up or notebook demonstrating that the numerical solution reproduces the stable time-dependent behaviour reported in the paper. Clear run instructions and parameter notes so you can reproduce results locally. Why I’m a good fit I have hands-on experience with stiff ODE systems, implicit solvers, Newton iterations, and numerical stability analysis. I focus on correctness, transparency, and making the implementation easy to extend or verify. Once you share the exact PDE and boundary conditions, I can confirm the discretisation choice and timeline. Best regards, Ammad

₹1,050 INR in 2 days