Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions

Table 1

Different radial basis functions.

Radial basis functions	𝜙(𝑟)	Parameters	Order
Gaussian	exp(−𝑐𝑟^2)	𝑐>0	𝑚≥0
Multiquadrics	(−1)^⌈𝛽⌉(𝑐^2+𝑟^2)^𝛽	𝛽>0,𝛽∉ℕ	𝑚≥⌈𝛽⌉
Inverse multiquadrics	(𝑐^2+𝑟^2)^𝛽	𝛽<0	𝑚≥0
Polyharmonic splines	(−1)^⌈𝛽/2⌉𝑟^𝛽	𝛽>0,𝛽∉2ℕ	𝑚≥⌈𝛽/2⌉
Polyharmonic splines	(−1)^𝑘+1𝑟^2𝑘log(𝑟)	𝑘∈ℕ	𝑚≥𝑘+1
Compactly supported	(1−𝑟)^4+(1+4𝑟)	𝑑≤3	𝑚≥0