pde - 如何在使用有限差分法求解 pde 集时修复 gPROMS 中的“系统结构奇异”错误？

Question

我是 gPROMS 的新手，并尝试使用 gPROMS 使用前向有限差​​分法求解给定的 pde 方程。

y"+z+y=0;

z'+y'=0;

y(0)=0, y'(0)=0, z(0)=1.

我已经为模型和流程编写了代码，如下所示：

变量类型

 ANY (lower bound 0; upper bound 100)

型号（问题）

#Defining independent variable
    DISTRIBUTION_DOMAIN
    x_dom AS [ 0 : 10 ]
    
#Defining dependent variables    
    VARIABLE
    y AS  DISTRIBUTION(x_dom) OF ANY
    z AS  DISTRIBUTION(x_dom) OF ANY
#Bondary condition    
    Boundary
    y(0)=0;
    z(0)=1;
    PARTIAL(y(0),x_dom)=0;
    
 #Writing pdes   
    Equation
    FOR x := 0|+ TO  10|- DO
    PARTIAL(y(x),x_dom,x_dom)+z(x)+y(x)=0;
    PARTIAL(z(x),x_dom)+PARTIAL(y(x),x_dom)=0;
    END

流程

 UNIT
    P101    AS  Problem
    SET
#Discretization method
    WITHIN P101 DO
    x_dom:= [ FFDM, 1, 10 ] ;
    END

结果

You need to ASSIGN 1 variable(s).
List of available variables:
 P101.y(0.0)     Algebraic (OUTPUT)
 P101.y(1.0)     Algebraic (OUTPUT)
 P101.y(2.0)     Algebraic (OUTPUT)
 P101.y(3.0)     Algebraic (OUTPUT)
 P101.y(4.0)     Algebraic (OUTPUT)
 P101.y(5.0)     Algebraic (OUTPUT)
 P101.y(6.0)     Algebraic (OUTPUT)
 P101.y(7.0)     Algebraic (OUTPUT)
 P101.y(8.0)     Algebraic (OUTPUT)
 P101.y(9.0)     Algebraic (OUTPUT)
 P101.y(10.0)    Algebraic (OUTPUT)
 P101.z(0.0)     Algebraic (OUTPUT)
 P101.z(1.0)     Algebraic (OUTPUT)
 P101.z(2.0)     Algebraic (OUTPUT)
 P101.z(3.0)     Algebraic (OUTPUT)
 P101.z(4.0)     Algebraic (OUTPUT)
 P101.z(5.0)     Algebraic (OUTPUT)
 P101.z(6.0)     Algebraic (OUTPUT)
 P101.z(7.0)     Algebraic (OUTPUT)
 P101.z(8.0)     Algebraic (OUTPUT)
 P101.z(9.0)     Algebraic (OUTPUT)
 P101.z(10.0)    Algebraic (OUTPUT)


WARNING: The system is structurally singular. gPROMS will try to weaken structural check and
         resolve the singularity on solver's level.
Structural Analysis: performing wellposedness check...

Structural analysis has found an error in the system

我尝试添加一个变量，但它不起作用。我应该如何编写代码以免出错？

谢谢你。

标签： pde