Many application problems in physics and financial mathematics have been modeled by differential equations of boundary value problems defined on large or infinite domains. Numerical solutions are often necessary since analytic solutions to such problems are rarely available. A Kevin's transformation that transforms an infinite domain to a finite one is one of approaches in dealing with infinite domain problems. In this paper, studies are carried out on when and how the transformation method can be applied to solve differential equations defined on large or infinite domains. Some new coupled transformation methods are proposed with convergence analysis. The proposed methods work well for certain problems, for example, that have reasonably decay rates. With the new approach, no artificial or truncated boundary conditions are needed. The key idea is to use a transformation to divide an infinite domain problem to a coupled two-domain problem that can be solved simultaneously. Convergence analysis provided some insights about conditions that the new methods can be applied to. Numerical examples are also presented to confirm the algorithm designs and analysis.