Truncation error in meshfree scheme
I try to solve a simple poisson equation using a code based on a meshfree 2D finite difference approach. The nodedistribution is uniform. Since the method approximates the function value at node "i" using N number of surrounding nodes based on their radial distance to node "i" I assume that the method can be seen as a central diffence approach. In ordinary finite difference method on uniform mesh, the central difference scheme gives one order higher for the even derivatives, isn't that right? In that case, should my code give the same rate of convergence (about 2) if I truncate the taylor series up to 2nd- or 3rd order? When I truncate the taylor series up to 4th order, the rate of convergence is about 4, which supports my theory that odd derivative terms cancel out due to uniform grid and central difference scheme.
This is what I now experience, but I'm not sure if my conclusion is correct. Any ideas?
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