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WA573

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derivative from finite difference...

WA573 70 Maple 2022
derivative differential-equations finite-difference
November 28 2023
1 1

Since (1/h)[f(i+1,t)-f(i,t)]=f(x,t)_{x} as h goes to zero, 'i' is the discrete index along x-axis. How to do it in Maple? How to reduce Eq. (5) into continuous derivatives?

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restart
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with(LinearAlgebra)
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with(PDEtools)
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with(Physics)
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with(plots)
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Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)
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``
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U := proc (i, t) options operator, arrow; Matrix([[1+I*(q(i+1, t)-q(i, t))/lambda, I*(r(i+1, t)-r(i, t))/lambda], [I*(r(i+1, t)-r(i, t))/lambda, 1-I*(q(i+1, t)-q(i, t))/lambda]]) end proc

proc (i, t) options operator, arrow; Matrix([[1+Physics:-`*`(Physics:-`*`(I, q(i+1, t)-q(i, t)), Physics:-`^`(lambda, -1)), Physics:-`*`(Physics:-`*`(I, r(i+1, t)-r(i, t)), Physics:-`^`(lambda, -1))], [Physics:-`*`(Physics:-`*`(I, r(i+1, t)-r(i, t)), Physics:-`^`(lambda, -1)), 1-Physics:-`*`(Physics:-`*`(I, q(i+1, t)-q(i, t)), Physics:-`^`(lambda, -1))]]) end proc

 (2)
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``
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V := proc (i, t) options operator, arrow; Matrix([[-((1/2)*I)*lambda, -r(i, t)], [r(i, t), ((1/2)*I)*lambda]]) end proc

proc (i, t) options operator, arrow; Matrix([[Physics:-`*`(Physics:-`*`(Physics:-`*`(Physics:-`*`(1, Physics:-`^`(2, -1)), I), lambda), -1), Physics:-`*`(r(i, t), -1)], [r(i, t), Physics:-`*`(Physics:-`*`(Physics:-`*`(1, Physics:-`^`(2, -1)), I), lambda)]]) end proc

 (3)
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NULL
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z := diff(U(i, t), t)+U(i, t).V(i, t)-V(i+1, t).U(i, t)

Matrix(%id = 4525182530)

 (4)
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z11 := simplify(lambda*z[1, 1]/h, size) = 0

I*(r(i+1, t)^2-r(i, t)^2+(D[2](q))(i+1, t)-(diff(q(i, t), t)))/h = 0

 (5)
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NULL

Download limit.mw

Residue for a function...

WA573 70 Maple 2022
residue physics
November 17 2023
0 0

Since C2=D1.D1inv should be equal to I. But return is just an expression (see attached). Further, how to obtain residue for a function C2?

residue.mw

How do I solve a differential equation i...

WA573 70 Maple 2022
eigenvalues differential-equations
January 10 2023
2 2
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restart
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with(DEtools); with(LinearAlgebra)
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diff(u(x, t), t) = [Matrix([[0, (1/2)*mu*k^2], [2*A^2-(1/2)*mu*k^2, 0]])]*u(x, t)

diff(u(x, t), t) = [Matrix(%id = 36893489823894642308)]*u(x, t)

 (1)
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"where u(x,t)=[u1 u2]^(T) is a vector. The solution of differential equation (1) is u=v*exp(w*t)."
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where*w^2 = -(1/4)*mu^2*k^4+mu*k^2*A^2
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"How can we solve differntial equation*(1) on Maple"?""

NULL

Download dsol.mw

Why the expression is too large?...

WA573 70 Maple 2022
solve
November 27 2022
1 0

Why the expression of lambda[1] is too large? One of the possible values of lambda[1] should be "sqrt(1/(4*omega^2 - 4))*a[-1]". 

JCN.mw 

Error, (in PDEtools/Normal) invalid inpu...

WA573 70 Maple 2022
simplification
November 18 2022
1 2

Why is the Maple giving this error. See attched file. Further, how can we eq. of the form "A+B`*sqrt(C) = 0" by eliminating the common denominator.

CM_TW.mw

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