Sir/Madam, How can I code the Laplace Adomian Decomposition method. Please help me. This is very important for my research purpose.

the procedure is, Lu(t)+Ru(t)+Nu(t)=g(t) L[Lu(t) ]+L[Ru(t) ]+L[Nu(t) ]=L[g(t)] s^n L[u(t) ]-s^(n-1) u(0)-s^(n-2) u^' (0)-…………-u^(n-1) (0)+L[Ru(t) ]+L[Nu(t) ]=L[g(t)] or, L[u(t) ]=u(0)/s+(u^' (0))/s^2 +⋯…………+(u^(n-1) (0))/s^n -1/s^n L[Ru(t) ]-1/s^n L[Nu(t) ]+1/s^n L[g(t)]. N(u)=∑_(n=0)^∞▒A_n A_n=1/n! d^n/(dλ^n ) [N(∑_(i=0)^∞▒〖λ^i u_i 〗) ]_(λ=0),n=0,1,2,……… L[∑_(n=1)^∞▒〖u_n (t)〗]=u(0)/s+(u^' (0))/s^2 +⋯…………+(u^(n-1) (0))/s^n -1/s^n L[R{∑_(n=1)^∞▒〖u_n (t) 〗}]-1/s^n L[∑_(n=1)^∞▒A_n ]+1/s^n L[g(t)]. L[u_0 (t)]=u(0)/s+(u^' (0))/s^2 +⋯…………+(u^(n-1) (0))/s^n +1/s^n L[g(t)] and L[u_(n+1) (t)]=-1/s^n L[〖R(u〗_n (t))]-1/s^n L[A_n ] .

[MINATI]

Dear susmita paul

I beleif you solved your problem. I have same problem. So can you share that program.

[e-mail]

Thanks

[Ffara Nara]

Is there anyone who can help me? I want to know the code of laplace adomiam decomposition method for system of differential equations. Thankyou.

[Ffara Nara]

Dear susmita paul and MINATI, can you help me? Thanks

Answer 1

[Prof. MUhammad Zeeshan]

use this piece of code

clear 
clc 
syms u u_0 
n = input('enter the number: '); 
y = input('enter the non-linear term in terms of u_0') ;
g1 = intpartgen(n); 
y1(1) = diff(y,1); 
result(1)=u_1*y1(1); 
for n2 = 2:n 
     n3=n2; 
    g = g1{n2+1}; 
y1(n2) = diff(y,n2); 
    b=g; 
    a = zeros(size(b)); 
    [m1,n1] = size(b); 
for k = 1:m1 
    [i1,j1,s1] = find(b(k,:)); 
        [m2,n2] = size(j1); 
j2(k) = n2; 
end 
    j3 = sort(j2); 
j3(m1+1) = 0; 
for k1 = 1:m1 
for k2 = 1:m1 
if j3(1,k1)==j2(1,k2)                

a(k1,:) = b(k2,:); 
if k11 
ft = factorial(t); 
                    t2 = strcat('(',t1,'^',num2str(t),'/',num2str(ft),')'); 
else 
                    t2 = t1; 
end 
if (strcmp(temp2,'')) 
                    temp2 = t2; 
elseif (strcmp(temp2(length(temp2)),'+')) 
                    temp2 = strcat(temp2,t2); 
else 
                    temp2 = strcat(temp2,'*',t2); 
end 
end 
end 
if j3(i1)==j3(i1+1) 
            temp2 = strcat(temp2,'+'); 
else 
term(i2) = sym(temp2); 
            temp2 = ''; 
            i2 = i2+1; 
end 
        i1 = i1+1; 
end 
l1=length(term); 
    t1=0; 
for k3=1:l1 
  t1 = t1+ term(k3)*y1(k3);             temp2 = strcat(temp2,'+'); 
end 
result(n3)= t1; 
end 
result ;

[aaditya chandel]

Unrecognized function or variable 'intpartgen'.

This error is coming.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/36437-integer-partition-generator