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 wish to know why this particular function is used? How this function is obtained?