(a) Design your own 3-stage explicit Runge-Kutta method with one-step error O(h4).

(b) Test your method by solving y′ = −y. Confirm that the global error in your numerical solution

is O(h3).

Write a Maple procedure that solves for y(1) in the initial value problem

                     y′ = f(y),     y(0) = 1,

using a numerical stencil based on the nth order Taylor series expansion of y. The procedure’s arguments should include an arbitrary function f, an integer n representing the accuracy of the Taylor series expansion, another integer N representing the number of steps between x = 0 and x = 1. Pick a test problem and compare your results with the output of dsolve/numeric.

Hello Maplers, i have encountered a little annoyance with Maple, that i would like to ask, whether it can be solved. 

It's when i try to define a function, like f(x)=2x and try to define it with a command f(x):=2x, a pop-up box comes up, asking me whether i'd like to use a 'function definition', or 'remember table assignment', and i would like to make Maple remember my choice that i want a function. 

I know i can write it like f:=x->2x, but i hate to look at that, to be frankly..

So, is there any way to solve this?

Please tell me how to do about the following problem to me.

g:=(b*y)^k*k*y;

simplify(%);

Then, what I obtained was (b*y)^k*k*y, not (b^k)*k*y^(k+1).

expand of the command brought the same answer not (b^k)*k*y^(k+1).

Please tell me what was wrong to my calculation.

Thank you in advance.

Taro.

How to solve this equation

cos(x)^2+2*x*cos(x)-2*sin(x)+4=0

with

solve(%,x) and evalf(%) ?

I get no solution. Is there any option to force Maple to solve this equation by solve and evalf?

Student[Calculus1]:-NewtonsMetnod(%,x=2) solves the problem.
If I use Series for sin(x) and cos(x) Maple can solve it too.

Thank you

Dear all,

A stupid question.

I tried to create a density plot of the data but I only saw the method to plot graphs through equations. (Actually, I'm not very familiar with related statistical commands in Maple)

This is the histograph of my data:

And I want to get the density plot like this:

It seems that we can get the graph through "InteractiveDataAnalysis" but cannot print the graph into the worksheet or assign the graph to the variable.

How to create a density plot through data? Thanks.

AOA... I want to export system of linear equation into matrix form...

Help.mw

restart:

Eq1:=S*diff(f(x,t),x,t)+diff(f(x,t),x)^2-f(x,t)*diff(f(x,t),x$2)=diff(f(x,t),x$3);

BCs := {D[1](f)(0,t)=cos(t), f(0,t)=0,D[1](f)(L,t)=0};

ICs := {f(x,0)=0};

S:=10:L:=5:
smod3:= pdsolve(Eq1,ICs union BCs,numeric,range=0..L);

smod3:-plot(t=0,  color=red):

it seems to me that the problem is due to the mixed bcs. Any way around?

Cheers!

Dear All,

I analyzed some example of linear equation systems and tried to distinguish the difference between the solve and fsolve in these cases.

1. In general case, the deviation between solve and fsolve is less than 10^-8, for example:

But, in some case, the deviation is more than 10^-7, for example:

how to reduce the error of solving the problem by fsolve?

2. It seems that solve will automatically translate the answer into numerical result while the system is composed with decimals, for example, we redo the second case with no decimals:

Is it possible to get the exact solution while the decimal is involved in the system?

The related file is attached. I'd appreciate any help on this topic. Thank a lot.

solve_and_fsolve.mw

Question_.pdf

this question about midpoint method I need help with the part c

thanks

I have the following nonlinear Differential Equation and don't know how to solve.  Can anyone give me any hints on how solvle for E__fd(t).  I don't even know the specific classification (other than nonlinear) of this DE can someone at least give me hint on that. Thanks.

.5*(diff(E__fd(t), t)) = -(-.132+.1*e^(.6*E__fd(t)))*E__fd(t)+0.5e-1

Thanks,

Melvin

I can't simplify the expression of 

(1/a[x])^(-k-1+epsilon)/(1/a[I])^(-k-1+epsilon)

to 

(a[x]/a[I])^(k+1-epsilon);

Please tell me how to do this.

Thank you in advance.

Taro yamada

1.which rules or theorems can guide to generate relations for words in group theory?

2.Is topological method such as complexes the direction to answer Question 1?

I am running a set of diffrential equation , but i receive below error

"Error, (in LL) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up"

I can't understand the problem

restart:

Eq1:=diff(f(x),x$4)+(f(x)*diff(f(x),x$3)-diff(f(x),x$1)*diff(f(x),x$2))=0;

Eq2:=diff(f2(x),x$2)+f(x)*diff(f2(x),x$1)=0;

bcs:=f(0)=0,(D@@2)(f)(0)=0,f(1)=0,D(f)(1)=1,f2(-1)=0.5,f2(1)=1;

dsolve({Eq1,Eq2,bcs},numeric,output = listprocedure);

Error, (in dsolve/numeric/process_input) boundary conditions specified at too many points: {-1, 0, 1},

can only solve two-point boundary value problems

How to handle such problem using dsolve?

Cheers!