Where to get started with Numerical Solutions to PDEs?

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SUMMARY

The discussion centers on the exploration of numerical solutions to nonlinear elliptic systems of partial differential equations (PDEs). The participant has a programming background in MATLAB and C++, along with a basic understanding of ordinary differential equation (ODE) numerical schemes. Recommendations include studying Finite Element techniques, particularly through modern resources, as older texts may not reflect current advancements. The suggestion to utilize online resources, such as Google, for references on nonlinear PDEs is also emphasized.

PREREQUISITES
  • Understanding of nonlinear elliptic systems of PDEs
  • Proficiency in MATLAB and C++ programming
  • Basic knowledge of ordinary differential equation (ODE) numerical schemes
  • Familiarity with Finite Element methods
NEXT STEPS
  • Research modern Finite Element analysis books applicable to specific programming languages
  • Explore online resources for numerical solutions to nonlinear PDEs
  • Study advanced numerical analysis techniques relevant to PDEs
  • Investigate the latest developments in Finite Element methods
USEFUL FOR

Mathematicians, engineers, and researchers interested in numerical methods for solving partial differential equations, particularly those with a background in programming and basic numerical analysis.

lmedin02
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I have established existence and uniqueness of solutions to a nonlinear elliptic system of PDE's and would like to see how the solutions look like numerically. I have some programming background on MatLab and C++. I also understand basic ODE numerical schemes. But I am not so sure, if I need to begin by first reading books on Numerical Analysis or is there a more direct way to learning about numerical solutions to my particular problem?

Thanks in advance for your discussion.
 
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I'm not an expert on numerical methods for PDE's but since you haven't received other replies, I'll suggest that you look at material on "Finite Element" techiques if they apply to your PDE's. The Finite Element books I have glanced at (such as the Shaum's book) are very concrete. You can probably find books that do Finite Element analysis in particular programming languages. I notice the wording in one of the Shaum's books implies that older books on Finite Elements are obsolete because of modern developments. I don't understand any details about that, but it wouldn't hurt to get a modern book.
 
Google 'nonlinear PDE'.
Let your fingers do the walking. There are several references to the numerical solution to nonlinear PDEs on the first page alone.
 

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