2">Numerical Solver</a></li><li><a href="#3">Numerical Solution of M = 20 and dt = 0.001</a></li><li><a href="#4">Numerical Solution of M = 40 and dt = 0.0003</a></li></ul></div><h2>Neumann-boundary-value Problem<a name="1"></a></h2><div><ul><li><img src="hw_1_4_2_eq13739371748068747965.png" alt="$v_t = \nu v_{xx}, x \in (0, 1), t &gt; 0$"></li><li><img src="hw_1_4_2_eq06405620194823022386.png" alt="$v(x, 0) = \cos(\pi x / 2), x \in [0, 1]$"></li><li><img src="hw_1_4_2_eq04074536036351455485.png" alt="$v(1,