52 lines
1.6 KiB
Python
52 lines
1.6 KiB
Python
""" Simple ODE problem. """
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# ===================================================== #
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# #
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# This script implements a simple first order ode. #
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# The FirstOrderODE class is defined inheriting from #
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# SpatialProblem. We denote: #
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# y --> field variable #
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# x --> spatial variable #
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# #
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# The equation is: #
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# dy(x)/dx + y(x) = x #
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# #
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# ===================================================== #
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from pina.problem import SpatialProblem
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from pina import Condition
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from pina.domain import CartesianDomain
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from pina.operators import grad
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from pina.equation import Equation, FixedValue
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import torch
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class FirstOrderODE(SpatialProblem):
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# variable domain range
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x_rng = [0., 5.]
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# field variable
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output_variables = ['y']
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# create domain
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spatial_domain = CartesianDomain({'x': x_rng})
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# define the ode
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def ode(input_, output_):
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y = output_
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x = input_
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return grad(y, x) + y - x
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# define real solution
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def solution(self, input_):
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x = input_
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return x - 1.0 + 2*torch.exp(-x)
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# define problem conditions
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conditions = {
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'BC': Condition(location=CartesianDomain({'x': x_rng[0]}), equation=FixedValue(1.)),
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'D': Condition(location=CartesianDomain({'x': x_rng}), equation=Equation(ode)),
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}
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truth_solution = solution |