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

조회 수: 19 (최근 30일)
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
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.

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답변 (1개)

Prof. MUhammad Zeeshan
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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