抄録
To correlate a large number of computational results into a compact analytical equation, an improved method is proposed for technical problems which have the two asymptotes y(0)→1 and y(∞)→x. When an analytical solution g(x) for a simple system is obtained, solutions of a family of similar problems can be approximated by the equation
y=G(xj))1/j (A)
in which a parameter j is determined so that Eq. (A) agrees with the exact value at x=1, thus
j=logg(1))/logy(1)
A recently proposed method of Churchill, Usagi and Ozoe is a special case of Eq. (A) with g(x)= 1+x.
The validity of the proposed method is confirmed in an application to simultaneous diffusion-reaction problems for various systems. It is interpreted that Eq. (A) describes a family of figures "similarly transformed" from an original g(x) with a similitude ratio 1/j on a logarithmic scale.
A method of rough but simple estimation of j is also discussed.
