Here I choose the integral font size nearer to 80% the current font size; the examples show a comparison with normal capitals and small caps.
\RequirePackage{fix-cm} % not needed if you use a scalable font
\documentclass{article}
\usepackage{xparse,xfp}
\makeatletter % we need to access @-commands
\NewDocumentCommand{\acr}{m}{{%
\fontsize{\fpeval{round(0.8*\f@size,0)}}{\f@baselineskip}\selectfont
#1%
}}
\makeatother
\begin{document}
nonlinear PDE system in \acr{FDM} or \textsc{fdm}
{\footnotesize nonlinear PDE system in \acr{FDM} or \textsc{fdm}}
\bigskip
{\LARGE nonlinear PDE system in \acr{FDM} or \textsc{fdm}}
\end{document}
If you change \fpeval{round(0.8*\f@size,0)}
into \fpeval{0.8*\f@size}
, to get 80% without rounding, you get
If you end up choosing small caps, you can avoid the burden of typing the acronym in lowercase letters:
\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\acr}{m}
{
\textsc{ \tl_lower_case:n { #1 } }
}
\ExplSyntaxOff
\begin{document}
nonlinear PDE system in \acr{FDM} or \textsc{fdm}
{\footnotesize nonlinear PDE system in \acr{FDM} or \textsc{fdm}}
\bigskip
{\LARGE nonlinear PDE system in \acr{FDM} or \textsc{fdm}}
\end{document}