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5

My first question: Will split ODE solvers likely work for my problem? From your description, this sounds like a textbook use-case for a split ODE solver. Neither an implicit method nor an explicit method is practical across the entire ODE. IMEX methods sound like a reasonable choice as long as the atmospheric temperature dynamics that you want to treat ...

3

(This answer is valid for both MATLAB and Octave, even though I mainly refer to MATLAB) There are two beasts to slay; but let's first understand the underlying data structure. MATLAB and Octave store sparse matrices in the coordinate (COO) format, i.e. a sparse matrix S is a collection of three arrays of the length equal to the number of nonzero entries of S:...

2

Assuming both the base and the exponent are integers, and the exponent is non-negative, the standard way of doing exponentiation is exponentiation by squaring. This technique is particularly effective when doing modular exponentiation (which is what is needed in asymmetric cryptography applications). Further, assuming that the exponent is known a priori and ...

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