V.Gnanaraj's blog

I have come accross an equation of the form ∂²u/∂x² + ∂²u/∂y² - K² u =0 with the following conditions. y ≥αx,y ≥-αx, x=H.How to solve this equation?.analytically.

In most of the research papers on meshless methods the following cubic spline function is used as weighting function.

 w(y) = 0  if y < -2,

w(y) =1/6(y+2)^3  ,    if -2 < y < -1 

w(y) =  2/3 – y^{^2}(1 + y/2) ,  if   -1 < y < 0

w(y)=   2/3 -y^{^2}(1 - y/2) , if   0 < y < 1

w(y) = -1/6 (y – 2 )^3  ,   if    1 < y < 2

w(y) = 0 if y >2

I am working in the area of microfuidics and wish to apply meshless methods to solve electroosmotic flow in microchannel. Can anybody suggest the journals which accepts papers on this field.

Key Words: Microfluidics, Navier-Stokes equations, microchannels, electroosmotic flow

How to solve the equation analytically

∂²u/∂x² + ∂²u/∂y² - K u =0

I am working in the field of microfluidics. I wish apply Reproducing Kernel Method to solve flow problems. Can anybody help me to send the paper "Reproducing Kernel Methods ", Wing Kam Liu, Sukky Jun, Yi Fei Zhang, International Journal for Numerical Methods in Fluids, Vol.