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as a brief explanation, I'm trying to solve a first order bessel equation which is part of a more complicated PDE problem, whose solution is as following form:

now we have a bunch of these functions and not one, so there are for example 10 integral coefficients like c1(1), c1(2),... and c2(1),c2(2),....

now when I apply the boundary conditions, a set of linear equations are made by which I can calculate c1, c2,... . in the form "A*C=B".

now as x is near zero, I1(x) goes to zero and K1(x) goes to inf, and as x goes up, I1(x) goes to inf and K1(x) goes to zero. given that y(x) is finite and something less than 0.07, c1 and c2 go to inf or zero depending on their factor. and here the problem begins. working with very high and low values decrease accuracy and might lead to inf or zero.

any idea to overcome this issue?

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