Can anyone suggest some good references for finite difference schemes to approximate $\frac{d^n y}{d x^n}, n = 1,2 \ldots,$ with non-uniform step size. I need to know for domain with singularities or jump, how the grids are more finer at the singularity and away from the singularity the grids are coarser.
finite difference method with non-uniform mesh
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ordinary-differential-equations
numerical-methods
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0What have you found thus far? – 2017-01-18
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0I found this book: Interfacial Fluid Mechanics: A Mathematical Modeling Approach, chapter 2, section 4.5. But this has not much. And also observe from this book is that the order of convergence also decreases with non-uniform grids. Can you suggest some references, if possible, how to implement it. – 2017-01-18