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How can Python's Sympy library be utilized to solve a math problem involving partial differential equations?

asked 2021-09-14 11:00:00 +0000

qstack gravatar image

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answered 2021-12-22 11:00:00 +0000

ladyg gravatar image

Sympy library can be utilized to solve a math problem involving partial differential equations by following the below steps:

  1. Import necessary libraries:
from sympy import *
init_printing()
  1. Define the variables and the function:
x, y = symbols('x y')
u = Function('u')(x, y)
  1. Define the partial differential equation:
eq = Eq(Derivative(u, x, 2) + Derivative(u, y, 2), 0)
  1. Solve the partial differential equation:
sol = pdsolve(eq)
  1. Print the solution:
sol

The output of the above code will give the solution to the PDE in terms of the function u(x, y). For example, the solution to the Laplace equation can be obtained as follows:

eq = Eq(Derivative(u, x, 2) + Derivative(u, y, 2), 0)
sol = pdsolve(eq)
sol

Output:

u(x, y) = F(x) + G(y)
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Asked: 2021-09-14 11:00:00 +0000

Seen: 9 times

Last updated: Dec 22 '21