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## Non-homogeneous and linear-differential-equation solutions (update:13-07-07)

version 1.0 (69.5 KB) by

homogen and non-homogen solution

Updated

DESCRIPTION;

This program is a running module for homsolution.m Matlab-functions. Also, differential non-homogeneous or homogeneous equations are solution possible the Matlab&Mapple Dsolve.m&desolve main-functions. But;

EXAMPLE;
[1]--+---Sometime mapple function is produce more short solution
|--- My function's solution:

[ R^4-4*R^3 ]*(y) = [5 ]
y = [ +exp^(4x).(C4)+exp^(0x).(C1+C2*x^1+C3*x^2) ]g + [-5/24*x^3-5/32*x^2-5/64*x-5/256 ]s
Generally solution Special solution
#### true ##### #### true #####
|
|--- Mapple's desolve function solution:

Dsolve('D4y-4*D3y-5=0','x')
ans =1/64*exp(4*x)*C1-5/24*x^3+1/2*C2*x^2+C3*x+C4
y= 1/64*exp(4*x)*C1 + 1/2*C2*x^2 + C3*x + C4 - 5/24*x^3
Generally solution Special solution (more short)
#### true ##### #### true #####

[2]---+---Matlab's Dsolve.m function is depend be selected input-veriables string character
|
|--- My function's solution:

>> homsolution([(R^4-16)^5*(R^2+1)*(R/(R^2+R+1))^2, x^20+x^10+sin(x)],0)
where R=[d/dx] and [f(R)].y = Q(x,y) differential equation solution

____Equation [1]

[ (R^4-16)^5*(R^2+1)*R^2/(R^2+R+1)^2 ]*(y) = [x^20+x^10+sin(x) ]
y= [ +exp^(-2x).(C20+C21*x^1+C22*x^2+C23*x^3+C24*x^4)+exp^(2ix)+ ...]g+ [ ...1/1518750*x*cos(x)^6+ ...]s

|
|--- Mapple's desolve function solution:

Dsolve('((Dy)^4-16)^5*((Dy)^2+1)*(Dy)^2/((Dy)^2+Dy+1)^2-(x^20+x^10+sin(x))=0','x')
(I don't advise , don't try this module, non-solution )

[3]---+---Sub-function running speed (for running 29-examples)
if you hide homsolution.m-lines(68,69,155,156) as fprintf,disp etc.. command then

My function is 1.602342 second (tic-toc & profiler control)
Matlab function is 1.094779 second

ALGORITHM;

--+--if Q(x,y)<> 0 than special solution
root value root-order degree
r1=R1 n1
r2=R2 n2
..... ....
rn=Rn nn
|---+---if root value = real
|
|----+---[max real root order degree]
else
|
Solution=1/[R-small root(1)]...
1/[R-small root(2)]...
1/[R-small root(n)]*[Q(x,y] (**)
where all step is first-order degree linear diff. equ. sol.
|---+---if root value = complex
|
|----+---[max complex root order degree]
else
|
Solution=1/[R-small root(1)]...
1/[R-small root(2)]...
1/[R-small root(n)]*[Q(x,y] (**)
where all step is first-order degree linear diff. equ. sol.

SYNTAX:

syntax.input : solution=regsolution.ouput (differential main function solution)
syntax.output: regsolt =conforming roots values for special solutions

EXAMPLE:
[ (R-2)^2*(R^2+1)^2*(R-1)^2 ]*(y) = [x^8 ]

Solution=
1.0000 2.0000
2.0000 2.0000
0 + 1.0000i 2.0000
0 - 1.0000i 2.0000

regsolt =

1.0000 firstly real roots
1.0000
2.0000
2.0000 --->look ALGORITHM<---
0 - 1.0000i
0 - 1.0000i
0 + 1.0000i secondly imaginer roots
0 + 1.0000i

Solution=[1/(R-1)][1/(R-1)][1/(R-2)][1/(R-2)][1/(R+sqrt(-1))] [1/(R+sqrt(-1))][1/(R-sqrt(-1))][1/(R-sqrt(-1))][ Q(x,y) ]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hi all,
the following code that i have written is giving error while i run it. can anyone help me to find out the bug?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

TT = 50*10^-9;
a = 0.2;

I0 = 6* 10^13;
z1 = 1.5*10^7;
z2 = 1.65* 10^6;
z = 2/(1/z1 + 1/z2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for i=1:1:150
t(i)= -1e-9+i/1e-9;
if (t(i) <= TT/2)
Ip(i) = I0*t(i)*2/TT ;
else
Ip(i)= I0 - 2* I0*(t(i) - TT/2)/TT;
end
sol(i) = Dsolve ('Dl = 2*p/z, D2l = (Ip(i)-(z/2+3/(4*a))*(Dl)^2)/(3*z/(4*a))', 'l(0) = 1e-10, p(0) = 1e5', 't(i)')
% Sol(i) = dsolve ('DL(t(i)) = 2*P(t(i))/z', 'DP(t(i))= (Ip-(3*P(t(i))/(2*a)+1)*(L(t(i))))/L(t(i))', 'L(0) = 1.*^-10', 'P(0) = 1.*^5', 't(i)');
%Solution = DSolve [{L'[t] ==2*P[t]/z, P'[t]==(Ip-(3*P[t]/(2*a)+1)*(L' [t]))/L[t], L[0] == 1.*^-10, P[0] == 1.*^5}, {P[t], L[t]}, {t, 0,3*TT}];
%Solution = NDSolve[L'[t] == 2*P[t]/z, L[t], {t, 0, 3*TT}];

end

i think it is awful, sorry but i just give a critic. i think it should be tidy n not make a guest confuse.thx

Ali Özgül

[1] In homsolution.m sub-function is appearing error: FOR may not be aligned with its matching END. But, this errors not appear my m-lint test and intersting this program running this m-lint error.

[2] Example.m main-file appear Help-warning error, But this file in possible, description, example and syntax-line

Why this errors appear? Can you send me submission this reason, I will be happy.

##### MATLAB Release
MATLAB 6.5.1 (R13SP1)