Sir/Madam, How can I code the Laplace Adomian Decomposition method. Please help me. This is very important for my research purpose.
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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 ] .
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Ffara Nara
2023년 9월 20일
Is there anyone who can help me? I want to know the code of laplace adomiam decomposition method for system of differential equations. Thankyou.
답변 (1개)
Prof. MUhammad Zeeshan
2022년 2월 6일
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 ;
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