Your assumption is frankly incorrect. Physics is generally expressed in terms of differential equations. This is not due to their analytical tractability - as

Your assumption is frankly incorrect. Physics is generally expressed in terms of differential equations. This is not due to their analytical tractability - as anyone who has attempted to solve PDEs before will know, most (nearly all) differential equations do not yield to analytical solution. Perhaps you think that quantum mechanics demands a discretized view of reality. This would be a complete misunderstanding of quantum mechanics, and physics in general.