3">Numerical Solution</a></li></ul></div><h2>Initial-boundary-value Problem<a name="1"></a></h2><div><ul><li><img src="hw_5_6_5_eq09646607200750628065.png" alt="$v_t + v_x = 0, x \in (0, 1), t &gt; 0$"></li><li><img src="hw_5_6_5_eq10837969092137167965.png" alt="$v(x, 0) = \sin^{80} \pi x, x \in [0, 1]$"></li><li><img src="hw_5_6_5_eq13655592921841104813.png" alt="$v(0, t) = v(1, t), t \geq 0$"></li><li>One Analytic Solution: <img src="hw_5_6_5_eq12424855783758455214.png" alt="$v = \sin^{80} (\pi (x - t))$"