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sử dụng các PDEtool để giải quyết PDE này và điền vào Bảng P9.8.1 với các lỗi tối đa tuyệt đối và số lượng của các nút cùng với những vấn đề 9.2 (d) để so sánh. Bạn có thể tham khảo Ví dụ 9,8 thủ tục để có được giá trị số của các lỗi tuyệt đối tối đa. | 456 PARTIAL DIFFERENTIAL EQUATIONS 9.8 PDEtool GUI Graphical User Interface of MATLAB for Solving PDEs a Consider the PDE 4 - 4 y 0 for 0 x 1 0 y 1 dx2 dxdy dy2 7 P9.8.1 with the boundary conditions 0 y ye2y 1 y 1 y e1 2y P9.8.2 x 0 xex x 1 x 1 ex 2 Noting that the field of coefficient c should be filled in as o Elliptic II c 4-2-2 1 4-2 1 in the PDE specification dialog box and the true analytical solution is x y x y ex 2y P9.8.3 use the PDEtool to solve this PDE and fill in Table P9.8.1 with the maximum absolute error and the number of nodes together with those of Problem 9.2 d for comparison. You can refer to Example 9.8 for the procedure to get the numerical value of the maximum absolute error. Notice that the number of nodes is the number of columns of p which is obtained by clicking Export_Mesh in the Mesh pull-down menu and then clicking the OK button in the Export dialog box. You can also refer to Example 9.10 for the usage of Adaptive Mesh but in this case you only have to check the box on the left of Adaptive Mode and click the OK button in the Solve Parameters dialog box opened by clicking Parameters in the Solve pull-down menu and then the mesh is adaptively refined every time you click the button in the tool-bar to get the solution. With the box on the left of Adaptive Mode unchecked in the Solve Parameters dialog box Table P9.8.1 The Maximum Absolute Error and the Number of Nodes The Maximum The Number Absolute Error of Nodes poisson 1.9256 41 X 41 PDEtool with Initialize Mesh PDEtool with Refine Mesh PDEtool with second Refine Mesh PDEtool with Adaptive Mesh PDEtool with second Adaptive Mesh 0.1914 177 PROBLEMS 457 the mesh is nonadaptively refined every time you click Refine Mesh in the Mesh pull-down menu. You can restore the previous mesh by clicking Undo Mesh Change in the Mesh pull-down menu. b Consider the PDE 2 5 Zu 0 for 0 x 4 0 y 4 P9.8.4 dx2 dy2 with the Dirichlet Neumann boundary conditions u 0 y ey cosy du x y dx x 4 ey sin4 e4cosy P9.8.5
