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<p>&nbsp;<span style="font-family: &quot;Times New Roman&quot;, serif; font-size: 10pt; text-align: justify;">The main purpose of this paper is to introduce a new method to obtain approximate solution to one phase Stefan problems. Several methods exist to solve these moving boundary problems. Each of them is mostly specific problem oriented and is not general enough to be applicable to a wide range of problems. The paper develops a front tracking finite difference method with variable time step. This variable time step method was suggested earlier, but without a well-defined complete methodology. For a fixed space step, first two time steps are obtained using collocation and/or Green&rsquo;s theorem of vector calculus. Subsequent step sizes are obtained by bisection of the discrete form of the Stefan condition. The method is general enough to be applicable to a broad class of moving boundary problems.</span></p> <p class="MsoNormal" style="text-align:justify;line-height:normal"><span style="font-size:10.0pt;font-family:&quot;Times New Roman&quot;,serif"><o:p></o:p></span></p>