Hi there,
When solving differential equations with Heaviside functions, a meijerg
function appears in the outcome, while a (simpler) expression is possible
as well. For example a beam problem:
*import sympy as spw = sp.symbols('w', cls=sp.Function)x =
sp.symbols('x')C1, C2, C3, C4 = sp.symbols('C1 C2 C3 C4') Q, a, b, EI =
sp.symbols('Q, a, b, EI')q = Q*(1 -
sp.Heaviside(x-a))+F*sp.DiracDelta(x-(a+b))diffeq =
sp.Eq(EI*sp.diff(w(x),x,4),q)w = sp.dsolve(diffeq)w = w.rhs*
*print(w)*
gives:
*C1 + x**3*(C4 - Q*Piecewise((Piecewise((0, Abs(x/a) < 1), (a*meijerg(((2,
1), ()), ((), (1, 0)), x/a), True)), a > 0), (Integral(Heaviside(-a + x),
x), True))/(6*EI) + 35*Heaviside(-a - b + x)/(6*EI)) + x**2*(C3 +
Q*Piecewise((Piecewise((0, Abs(x/a) < 1), (a**2*meijerg(((3, 1), ()), ((),
(2, 0)), x/a), True)), a > 0), (Integral(x*Heaviside(-a + x), x),
True))/(2*EI) - 35*a*Heaviside(-a - b + x)/(2*EI) - 35*b*Heaviside(-a - b +
x)/(2*EI)) + x*(C2 - Q*Piecewise((Piecewise((0, Abs(x/a) < 1),
(a**3*meijerg(((4, 1), ()), ((), (3, 0)), x/a), True)), a > 0),
(Integral(x**2*Heaviside(-a + x), x), True))/(2*EI) + 35*(a +
b)**2*Heaviside(-a - b + x)/(2*EI)) + Q*x**4/(24*EI) +
Q*Piecewise((Piecewise((0, Abs(x/a) < 1), (a**4*meijerg(((5, 1), ()), ((),
(4, 0)), x/a), True)), a > 0), (Integral(x**3*Heaviside(-a + x), x),
True))/(6*EI) - 35*(a + b)**3*Heaviside(-a - b + x)/(6*EI)*
Thus including meijerg functions.
If the same result is found by integrating multiple times with
meijerg=False:
*import sympy as spw = sp.symbols('w', cls=sp.Function)x =
sp.symbols('x')C1, C2, C3, C4 = sp.symbols('C1 C2 C3 C4') Q, a, b, EI =
sp.symbols('Q, a, b, EI')q = Q*(1 -
sp.Heaviside(x-a))+F*sp.DiracDelta(x-(a+b))V =
sp.integrate(-q,x,meijerg=False)+C1M =
sp.integrate(V,x,meijerg=False)+C2kappa = M / EIphi =
sp.integrate(kappa,x,meijerg=False)+C3w =
sp.integrate(-phi,x,meijerg=False)+C4print(w)*
the following result is obtained:
*-C3*x + C4 - (C1*x**3/6 + C2*x**2/2 - Q*(x**4/24 - (a**4/24 - a**3*x/6 +
a**2*x**2/4 - a*x**3/6 + x**4/24)*Heaviside(-a + x)) - 35*(-a*x**2/2 +
a*x*(a + b) - a*(a + b)**2/2 - b*x**2/2 + b*x*(a + b) - b*(a + b)**2/2 +
x**3/6 - x*(a + b)**2/2 + (a + b)**3/3)*Heaviside(-a - b + x))/EI*
Would it be possible to implement a meijerg=false option for dsolve as well?
Kind regards,
Tom van Woudenberg
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