M_{K}=\frac{1}{2^{k+1}-2}\sum_{i=0}^{L-1}\sum_{l=1}^{K}\binom{K}{l}h_{i}i^{l}M_{K-l}
M_0=1 and the size of h_i is L.
I tried to compute this summation in matlab, my attempt is as following:
clear
h=[ (1+sqrt(3))/4 (3+sqrt(3))/4 (3-sqrt(3))/4 (1-sqrt(3))/4]';
% for simplicity i take...
Actually my codes are working accurately when B.C.s are dirichlet, but when B.C.s are turned to Neumann i confused how to edit the codes anyway i will look your codes.
Thank you jfgobin for your help.
You are right about
T=T(:,1);. It ought to be T=T(:,end);.
I want to show what i did so i multiplied by 0 because of u'_x(0,t)=0.
I put T(m+1,j)=2; just after second for loop but still i can't get correct results.
I am trying to solve the following pde numerically using backward f.d. for time and central di fference approximation for x, in MATLAB but i can't get correct results.
\frac{\partial u}{\partial t}=\alpha\frac{\partial^{2}u}{\partial x^{2}},\qquad u(x,0)=f(x),\qquad u_{x}(0,t)=0,\qquad...
I am looking for a software that can compute the following integral
∫_0^1f(x)\phi(2^jx-k)dx.
\phi(x) is scaling function of a wavelet family (especially Daubechies), j and k are scaling and translation parameters respectively.
I substituted
\psi(t)=[∑_k(−1)^kc_k\phi(2t+k−N+1)]
into
∫t\psi(t)dt.
Then i got
∫t[∑_k(−1)^kc_k\phi(2t+k−N+1)]dt=∑_k(−1)^kc_k∫t\phi(2t+k−N+1)]dt=0.
Actually i am not sure how to find the above integral but i did some change of variables and used integration by parts...
i can see 5.14 but i can not obtain 5.15 and 5.16.
Actually i get \sum_k (-1)^kc_k.0=0 instead of \sum_k (-1)^k k^p c_k=0 from the integral ∫t^p [\sum_k (-1)^kc_k \phi(2t+k-N+1)]dt=0.
Homework Statement
B(u,u)=\int_{0}^{L}a\frac{du}{dx}\frac{du}{dx}dx
B(.,.) is bilinear and symmetric, δ is variational operator.
In the following expression, where does \frac{1}{2} come from? As i know variational operator is commutative why do not we just pull δ to the left?
B(\delta...
I am trying to understand Ritz method, but i have troubles wtih determining the boundary conditions. After weak formulation of a differential equation how do we determine natural and essential b.c.?
What are boundary terms, secondary variables, primary variables, natural and essential...