统计代写|R代写project|ODE/MOL routine

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统计代写|R代写project|ODE/MOL routine

pdela called in the main program of Listing $3.1$ follows.
pdela=function ( $t, u$, parm) {
$#$

$V 1(x, t), V 2(x, t), V 3(x, t), C 1(t), C 2(t), C 3(t)$

$#$

One vector to three vectors, three scalars

pdela called in the main program of Listing $3.1$ follows.
pdela=function $(t, u$, parm) {
$#$ # Function pdela computes the $t$ derivatives of
$# \mathrm{~V} 1(\mathrm{x}, \mathrm{t}), \mathrm{V} 2(\mathrm{x}, \mathrm{t}), \mathrm{V} 3(\mathrm{x}, \mathrm{t}), \mathrm{C} 1(\mathrm{t}), \mathrm{C} 2(\mathrm{t}), \mathrm{C} 3(\mathrm{t})$
$#$
$#$ One vector to three vectors, three scalars
$\mathrm{V} 1=\mathrm{rep}(0, \mathrm{nx}) ;$
$\mathrm{V} 2=\mathrm{rep}(0, \mathrm{nx}) ;$
$\mathrm{V} 3=\mathrm{rep}(0, \mathrm{nx}) ;$
for $(i$ in $1: \mathrm{nx}){$
$\mathrm{V} 1[i]=u[i] ;$
$\mathrm{V} 2[i]=u[i+n x] ;$
$\mathrm{V} 1=\operatorname{rep}(0, \mathrm{nx})$;
V2 $=$ rep $(0, n \mathrm{x})$;
$\mathrm{V} 3=\operatorname{rep}(0, \mathrm{nx})$;
for (i in $1: n x){$
$\mathrm{V} 1[\mathrm{i}]=\mathrm{u}[\mathrm{i}]$;
$\mathrm{V} 2[i]=\mathrm{u}[i+n \mathrm{x}]$;

统计代写|R代写project|ODE/MOL routine for eqs

We can note the following details about Listing $3.2$.

• The function is defined.
pdela=function (t, u, parm) {
$#$
Function pdela computes the t derivatives of

$# \mathrm{~V} 1(\mathrm{x}, \mathrm{t}), \mathrm{V} 2(\mathrm{x}, \mathrm{t}), \mathrm{V} 3(\mathrm{x}, \mathrm{t}), \mathrm{C} 1(\mathrm{t}), \mathrm{C} 2(\mathrm{t}), \mathrm{C} 3(\mathrm{t})$
$t$ is the current value of $t$ in eqs. (3.1), (3.2), (3.3). $\mathrm{u}$ is the 66-vector of ODE/PDE
dependent variables. parm is an argument to pass parameters to pdela (unused,
but required in the argument list). The arguments must be listed in the order stated
to properly interface with I sodes called in the main program of Listing 3.1. The
derivative vector of the LHS of eqs. $(3.1),(3.2),(3.3)$ is calculated and returned
to Isodes as explained subsequently.

• Vector u is placed in three vectors and three scalars to facilitate the programming
of eqs. (3.1), (3.2), (3.3).
#
One vector to three vectors, three scalars

$\mathrm{V} 1=\operatorname{rep}(0, \mathrm{nx})$;
$\mathrm{V} 2=r \operatorname{ep}(0, \mathrm{nx})$;
$\mathrm{V} 3=\operatorname{rep}(0, \mathrm{nx})$;
for (i in $1: n x$ ) {
$\mathrm{V} 1[i]=\mathrm{u}[\mathrm{i}] ;$

$\mathrm{V} 2[i]=\mathrm{u}[i+\mathrm{nx}]$;
$\mathrm{V} 3[i]=\mathrm{u}[i+\mathrm{nx} * 2]$;
}
$\mathrm{Cl}=\mathrm{u}[3 * \mathrm{nx}+1] ;$
$\mathrm{C} 2=\mathrm{u}[3 * \mathrm{nx}+2]$;
$C 3=u[3 * n x+3]$;
$\mathrm{V} 2[i]=\mathrm{u}[i+\mathrm{nx}] ;$
$\mathrm{V} 3[i]=\mathrm{u}[i+\mathrm{nx} \star 2] ;$
$\mathrm{C} 1=\mathrm{u}[3 * \mathrm{nx}+1] ;$
$\mathrm{C} 2=\mathrm{u}[3 * \mathrm{nx}+2] ;$
$\mathrm{C} 3=\mathrm{u}[3 * \mathrm{nx}+3] ;$
$\frac{\partial V_{1}(x, t)}{\partial x}=\mathrm{V} 1 \mathrm{x}, \frac{\partial V_{2}(x, t)}{\partial x}=\mathrm{V} 2 \mathrm{x}, \frac{\partial V_{3}(x, t)}{\partial x}=\mathrm{V} 3 \mathrm{x}$ are computed by
dss004 a library routine for first order spatial derivatives. dss004 is listed in
Appendix Al with an explanation of the arguments.
#

V1x, $\mathrm{V} 2 \mathrm{x}, \mathrm{V} 3 \mathrm{x}$

$\mathrm{V} 1 \mathrm{x}=\mathrm{dss} 004(\mathrm{x} 1, \mathrm{xu}, \mathrm{nx}, \mathrm{V} 1) ;$
$\mathrm{V} 2 \mathrm{x}=\mathrm{dss} 004(\mathrm{x} 1, \mathrm{xu}, \mathrm{nx}, \mathrm{V} 2) ;$
$\mathrm{V} 3 \mathrm{x}=\mathrm{dss} 004(\mathrm{x} 1, \mathrm{xu}, \mathrm{nx}, \mathrm{V} 3) ;$

• $\frac{\partial V_{1}(x, t)}{\partial x}=\mathrm{V} 1 \mathrm{x}, \frac{\partial V_{2}(x, t)}{\partial x}=\mathrm{V} 2 \mathrm{x}, \frac{\partial V_{3}(x, t)}{\partial x}=\mathrm{V} 3 \mathrm{x}$ are computed by dss 004 a library routine for first order spatial derivatives. dss 004 is listed in Appendix Al with an explanation of the arguments.
$#$
V1x, V2x, V3x

$\mathrm{V} 1 \mathrm{x}=\mathrm{dss} 004(\mathrm{xl}, \mathrm{xu}, \mathrm{nx}, \mathrm{V} 1)$;
$\mathrm{V} 2 \mathrm{x}=\mathrm{dss} 004(\mathrm{xl}, \mathrm{xu}, \mathrm{nx}, \mathrm{V} 2)$;
$\mathrm{V} 3 \mathrm{x}=\mathrm{dss004}(\mathrm{xl}, \mathrm{xu}, \mathrm{nx}, \mathrm{V} 3)$;

统计代写|R代写project|Numerical, graphical output

For the case of no cross diffusion, chi2 =chi $3=0$ in Listing 3.1, the output is the same as in Table $2.3$. This case is worth executing since if the output changes from Table $2.3$, a programming error would be indicated.

The following abbreviated numerical output is for cross diffusion included, chi $2=$ chi $3=1$. $0 \mathrm{e}-04$ in Listing $3.1$.
We can note the following details of Table $3.1$.

• The output is for 21 values of $t$ corresponding to nout $=21$ in Listing 3.1, that is, $\mathrm{t}=0,48, \ldots 240$ with every fourth value of $t$ displayed.
• The output is for $66+1=67$ values in the solution vectors of out from lsodes as discussed previously.
• Homogeneous ICs at $t=0$ are confirmed, $V_{1}(x, t=0)=V_{2}(x, t=0)=$ $V_{3}(x, t=0)=C_{1}(t=0)=C_{2}(t=0)=C_{3}(t=0)=0$.
• $V_{2}(x, t)=V_{3}(x, t)$ since the parameters are the same for these two dependent variables. This is a worthwhile check since a difference in these solutions would indicate a programming error.
• Similarly, $C_{2}(t)=C_{3}(t)$ since the parameters are the same for these two dependent variables. Again, this is a worthwhile check since a difference in these solutions would indicate a programming error.
• The solutions are significantly different with cross diffusion added to eqs. (3.2-1), (3.3-1) as indicated by a comparison of Tables $2.3$ and 3.1.
• The computational effort for the integration of the 66 ODEs is modest, ncall $=334 .$
The graphical output is in Figs. 3.1.
A comparison of Fig. 2.1-1 and Fig. 3.1-1 indicates that the cross diffusion has a negligible effect on $V_{1}(x, t)$.

A comparison of Fig. 2.1-2 and Fig. 3.1-2 indicates that the cross diffusion has a negligible effect on $C_{1}(t)$.

A comparison of Fig. 2.2-1 and Fig. 3.1-3 indicates that the cross diffusion reduces the variation of $V_{2}(x, t)$ with $x$ (by the substraction of the cross diffusion term in $D_{V 2} \frac{\partial^{2} V_{2}(x, t)}{\partial x^{2}}-\chi_{2} \frac{\partial^{2}\left(V_{2}(x, t) V_{3}(x, t)\right)}{\partial x^{2}}$ in eq. $\left.(3.2-1)\right)$.

A comparison of Fig. $2.2-2$ and Fig. 3.1-4 indicates that the cross diffusion reduces the increase of $C_{2}(t)$ with $t$ (the effect of $\mathrm{BC}(3.1-2)$ is reduced).

A comparison of Fig. 2.2-3 and Fig. 3.1-5 indicates that the cross diffusion reduces the flux of $C_{2}(t)$.

The graphical output for component 3 is the same as for 2 and is not included here. That is, the preceding conclusions apply to $V_{3}(x, t), C_{3}(t)$ (since $V_{3}(x, t)$ is the same as $V_{2}(x, t)$ and $C_{3}(t)$ is the same as $C_{2}(t)$ for the parameters in Listing 3.1).

统计代写|R代写project|ODE/MOL routine

pdela=function ( t,u , parm) {
##

##

统计代写|R代写project|ODE/MOL routine for eqs

• 功能已定义。
pdela=function (t, u, parm) {
##
函数 pdela 计算 t 的导数

# \mathrm{~V} 1(\mathrm{x}, \mathrm{t}), \mathrm{V} 2(\mathrm{x}, \mathrm{t}), \mathrm{V} 3(\mathrm{x}, \mathrm{t}), \mathrm{C} 1(\mathrm{t}), \mathrm{C} 2(\mathrm{t}), \mathrm{C} 3(\mathrm{t})# \mathrm{~V} 1(\mathrm{x}, \mathrm{t}), \mathrm{V} 2(\mathrm{x}, \mathrm{t}), \mathrm{V} 3(\mathrm{x}, \mathrm{t}), \mathrm{C} 1(\mathrm{t}), \mathrm{C} 2(\mathrm{t}), \mathrm{C} 3(\mathrm{t})
t是eqs的当前值。(3.1)、(3.2)、(3.3)。是 ODE/PDE因变量的 66 向量。parm 是将参数传递给 pdela 的参数（未使用，但在参数列表中是必需的）。参数必须按规定的顺序列出，以便与清单 3.1 的主程序中调用的 I 节点正确连接。eqs 的 LHS 的导数向量。并返回到 Isodes，如下所述。tu(3.1),(3.2),(3.3)

• 向量 u 被放置在三个向量和三个标量中，以方便
eqs 的编程。(3.1)、(3.2)、(3.3)。
#
一个向量到三个向量，三个标量

V1=rep⁡(0,nx) ; ; ; for (i in ) {
V2=rep⁡(0,nx)
V3=rep⁡(0,nx)
1:nx
V1[i]=u[i];

V2[i]=u[i+nx] ; ; } ; ; 计算如下
V3[i]=u[i+nx∗2]Cl=u[3∗nx+1];
C2=u[3∗nx+2]
C3=u[3∗nx+3]
V2[i]=u[i+nx];
V3[i]=u[i+nx⋆2];
C1=u[3∗nx+1];
C2=u[3∗nx+2];
C3=u[3∗nx+3];
∂V1(x,t)∂x=V1x,∂V2(x,t)∂x=V2x,∂V3(x,t)∂x=V3x
dss004 一阶空间导数的库例程。dss004 列在

#

V1x,V2x,V3x

V1x=dss004(x1,xu,nx,V1);
V2x=dss004(x1,xu,nx,V2);
V3x=dss004(x1,xu,nx,V3);

• ∂V1(x,t)∂x=V1x,∂V2(x,t)∂x=V2x,∂V3(x,t)∂x=V3x } dss 004 是一阶空间导数的库例程。dss 004 列在附录 A 中，并附有参数说明。
##
V1x、V2x、V3x

V1x=dss004(xl,xu,nx,V1) ; ; ;
V2x=dss004(xl,xu,nx,V2)
V3x=dss004(xl,xu,nx,V3)

统计代写|R代写project|Numerical, graphical output

3.1

• 输出对应于清单 3.1 中的 nout值，即显示每四个值。t=21t=0,48,…240t
• 如前所述，输出来自 lsodes 的解向量中的6666+1=67
• 确认时的同质 IC。t=0V1(x,t=0)=V2(x,t=0)= V3(x,t=0)=C1(t=0)=C2(t=0)=C3(t=0)=0
• V2(x,t)=V3(x,t)因为这两个因变量的参数相同。这是一项有价值的检查，因为这些解决方案的差异表明存在编程错误。
• 同样，因为这两个因变量的参数相同。同样，这是值得检查的，因为这些解决方案的差异表明存在编程错误。C2(t)=C3(t)
• 解决方案与添加到 eqs 的交叉扩散显着不同。(3.2-1), (3.3-1) 如表和 3.1 的比较所示。2.3
• 66 个 ODE 的积分计算量不大，ncall图形输出如图。3.1。图 2.1-1 和图 3.1-1 的比较表明交叉扩散对的影响可以忽略不计。=334.V1(x,t)

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