All Questions
Tagged with mathematica maple
40
questions
1
vote
0
answers
33
views
Sum with constraints in maple or mathematica [closed]
I'm looking for a code in Maple or Mathematica to evaluate and give a list of terms in expressions like
$\newcommand{\on}[1]{\operatorname{#1}}$
$$
\sum_{a\ +\ b\ +\ c\ =\ 6}\on{f}\left(a\right)\on{f}\...
- 13
1
vote
0
answers
42
views
How to define a linear operator in Maple that commutes with derivatives?
I would like to simplify an expression involving the Hilbert transform in Maple. The Hilbert transform is defined by $$ Hf(x) = \frac{1}{\pi} \ \mathrm{p.v.} \int_{-\infty}^{+\infty} \frac{f(z)}{z-x} \...
- 11
1
vote
0
answers
83
views
Conditions on the coefficients that the roots of a polynomial be less that or equal to unity in absolute value
Consider the polynomial $$f(x)=p_0x^n+p_1x^{n-1}+...+p_{n-1}x+p_n,~p_i \in \mathbb C.$$
Particularly, in the case of absolute stability of a multi-step numerical method, how can we find out the ...
- 2,184
3
votes
1
answer
139
views
How to do a fast numerical computation of an oscillatory integral including $\operatorname{HeunC}$ function using Mathematica?
I am trying to numerically compute the following integral in Mathematica
$$\int_{1}^{1000} dx \,(x+2)e^{-2Ia(x+2)}\operatorname{HeunC}[-4Ib,-4Ib,1+4Ib,1,-4Ib,-x/2]$$
where $\operatorname{HeunC}$ is ...
- 31
1
vote
1
answer
141
views
How to calculate the following expectation and variance?
Given
$$X_1 \sim N(\mu_1, \sigma_1^2),$$
$$X_2 \sim N(\mu_2, \sigma_2^2),$$
$$X_1 \mathrm{\ and\ } X_2 \mathrm{\ are\ independent}.$$
and
$$Y = \max(\max(X_1,0) + X_2, 0),$$
find
$$E(Y) \mathrm{\ \ ...
- 37
2
votes
1
answer
133
views
Zero equivalence in computer algebra systems
Testing whether an expression (say, on the real or complex numbers), with or without variables, is known to be difficult. There is an semi-algorithm by Daniel Richardson to solve it for the exp–log ...
- 825
-1
votes
3
answers
54
views
plotting a function i
How can i plot bellow function in MAPLE or MATHEMATICA or MATLAB?
$$y=0.05+0.1\cdot e^{0.01x}\cdot \cos(0.2\cdot x)$$
while $x$ can be in the range of $ -350$ to $+350$ or less.
Thank you
0
votes
0
answers
217
views
Computational examples in differential geometry using Mathematica, Matlab, Maple etc. with visualization possible
I want to master the computing "apparatus" of differential geometry. Some theoretical sections are already very difficult to assimilate, and without visual calculations it is almost impossible to ...
- 731
0
votes
2
answers
177
views
General 2nd order ODE with non-constant coefficient
I'm trying to solve the general case of second order ODE: $y''(t) + p(t)y'(t) + q(t)y(t) = 0$.
where $p(t)$ and $q(t)$ are polynomials divides contains some symbolic constant and $t$,$t^2$,$t^3$ and $...
- 13
1
vote
0
answers
797
views
best way to plot the 3D shape made by many intersecting f(x,y,z) functions?
What's the best way to use a computer to plot the 3D shape made by many intersecting f(x,y,z) functions?
I was trying to do something like the following, except I still have not idea what the shape ...
- 351
1
vote
1
answer
170
views
If analytical solvers fail in solving an ODE, does it mean that it is unlikely have an analytical solution?
If analytical solvers (For example, Mathematica and Maple) fail to solve an ODE (Here, I have such situation with the ODE I have given in this question: second order ODE with time-dependent ...
- 161
1
vote
1
answer
3k
views
Analytical solution for convection diffusion equation
Convection-diffusion equation is:
$\frac{\partial u}{\partial t} + \frac{\partial u}{\partial x} = 0.01\frac{\partial^2 u}{\partial x^2}$
Inital conditon is:
$u(x,0) = sin(x)$ over the domain 0 to $...
- 215
1
vote
0
answers
206
views
Multivariate recurrence solve
I am currently working on a project and have reduced much of the problem to a single recurrence equation:
$$g(x,y)=1-\frac{1}{6}g(y,x-1)-\frac{1}{2}g(y,x)-\frac{1}{3}g(y+1,x-1)$$
$$g(0,a)=1$$
$$g(a,0)...
- 111
0
votes
1
answer
64
views
How to define a funciton without the explicit defination in Maple?
I want to define a funtion in Maple like:
g(t,r,theta,phi)
but without the explicit defination.
Thus, when I try to run
diff(g,t)
I hope it can give(only the formular, not(also it cant) the ...
- 15
0
votes
2
answers
390
views
Maple and Mathematica disagree using dsolve for system of ODE initial value problem
I'm trying to solve a system of ODEs, symbolically, using Maple and Mathematica. I'm actually comparing the analytic solution with a numerical one (this is for a large simulation project, of which ...
- 111