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These are questions asked by WA573

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?






Setup(mathematicalnotation = true)

[mathematicalnotation = true]



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



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



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

Matrix(%id = 4525182530)


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



Download limit.mw

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?



with(DEtools); with(LinearAlgebra)

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)


"where u(x,t)=[u1 u2]^(T) is a vector. The solution of differential equation (1) is u=v*exp(w*t)."

where*w^2 = -(1/4)*mu^2*k^4+mu*k^2*A^2

"How can we solve differntial equation*(1) on Maple"?""


Download dsol.mw

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]". 


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.


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