In this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; vt+vvx-vxx=0, x0, t0,v(x,0)=u+, x0,v(0,t)=ub, t0,$matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,,,,x 0,,,,t 0,} cr {vleft( {x,0} right) = {u_ + },,,,x 0,} cr {vleft( {0,t} right) = {u_b},,,t 0,} cr }$ where x and t represent distance and time, respectively, and u + is an initial condition, ub is a boundary condition which are constants ( u + ≠ ub ). Analytic solution of above problem is solved depending on parameters ( u + and ub ) then compared with numerical solutions to show there is a good agreement with each solutions.
展开▼
