## 15 Reputation

8 years, 233 days

## Characteristic relation for linear ODE s...

Maple 2015

hi.for linear coupling equation

dsys3 := {-72.49829200*(diff(f1(x), x, x))+0.8377580411e-2*(diff(f2(x), x))-8.873545400*10^9*(diff(f3(x), x))+2.114533515*10^18*f1(x), -878.8477313*(diff(f2(x), x, x))+1.590065471*10^20*f2(x)-7.353421206*10^(-26)*(diff(f3(x), x, x))+4.891459762*10^10*f3(x), 4.027667395*10^(-20)*(diff(f3(x), x, x, x, x))-0.6274394007e-2*(diff(f3(x), x, x))+8.873545401*10^9*(diff(f1(x), x))-7.352113720*10^(-26)*(diff(f2(x), x, x))+4.904509456*10^10*f2(x)+1.208381068*10^19*f3(x)-2.499990383*10^26*omega*(diff(f3(x), x, x))}

by assuming and to expand these functions(f1-f2-f3) in polynomial form(e.g. Chebyshev, power polynomials, Legendre and etc).:

f1(x):=(&sum;)H[i] *(e)^(lambda[i] *x); f2(x):=(&sum;)alpha[i]*H[i] *(e)^(lambda[i] *x);f3(x):=(&sum;)GAMMA[i]*H[i] *(e)^(lambda[i] *x)

how i detemine lambda[i] which are roots of the  characteristic equations?in other word how i can build characteristic relation for coupling equation?

2)how i can gain value for alpha[i] and GAMMA[i]

by using equation

Q1 := subs(x = 0, sum(H[i]*exp(lambda[i]*x), i = 1 .. 8)); Q2 := subs(x = L, sum(H[i]*exp(lambda[i]*x), i = 1 .. 8)); Q3 := subs(x = 0, sum(alpha[i]*H[i]*exp(lambda[i]*x), i = 1 .. 8)); Q4 := subs(x = L, sum(alpha[i]*H[i]*exp(lambda[i]*x), i = 1 .. 8)); Q5 := subs(x = 0, sum(GAMMA[i]*H[i]*exp(lambda[i]*x), i = 1 .. 8)); Q6 := subs(x = L, sum(GAMMA[i]*H[i]*exp(lambda[i]*x), i = 1 .. 8)); M := diff(sum(GAMMA[i]*H[i]*exp(lambda[i]*x), i = 1 .. 8), x); Q7 := subs(x = 0, M); Q8 := subs(x = L, M)

????

thanks...

## Problem with dsolve...

Maple 18

hi.please see attached file and help me

"initial Newton iteration is not converging" in dsolve cople equations

thaks..FEREKANS2.mw

## Error with indices(res, nolist)...

hi .please see attached file below and help me

thanks..indices(res_nolist).mw

## find root method...

Maple 18

hi every one..

how i solve numerically  couple equations which attached below .in solve this equation we must  starting from a very small value of V(voltage) with initial guesses for x1 and x3

near zero and using find root method.it is noted that  the solution at this voltage step are used as initial guesses

for the next voltage step, and the process is repeated..

thanks

2DOF.mw

## Singularity in dsolve/numeric/bvp...

Maple

mid_point.mw

hi i a have a problem with program which attached..please help me

thanks alot

dsys3 := {(diff(w(x), x, x, x, x))/x^2 = .4/(x^3*(1-w(x))^3)+40*(1+.65*(1-w(x)))/(x*(1-w(x))^2), w(0) = 0, w(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0}

dsol5 := dsolve(dsys3, numeric, output = array([.5]))

Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

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