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Text 11

The document presents two partial differential equations describing the relationships between u1, u2, x, and t. The equations are solved over the intervals of 0 to 1 for x and 0 to 20 for t, with initial conditions of u1=0 and u2=0 and specified boundary conditions. Constants in the equations are set to pec=pet=7, y=10, c=2.5, da=0.1, and r=0.5.

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gverma9461
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54 views4 pages

Text 11

The document presents two partial differential equations describing the relationships between u1, u2, x, and t. The equations are solved over the intervals of 0 to 1 for x and 0 to 20 for t, with initial conditions of u1=0 and u2=0 and specified boundary conditions. Constants in the equations are set to pec=pet=7, y=10, c=2.5, da=0.1, and r=0.5.

Uploaded by

gverma9461
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as TXT, PDF, TXT or read online on Scribd
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du1/dt=(1/pec)*d2u1/dx2-du1/dx-da*(1+u1)*exp(y*u2/(1+u2))

du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0
K 'WS 'ILJ [87 [09 I[8 U- 8 U- 8U -98 U - 98 [8 U -98 U [98 P

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2uWQKJH QLKJQNKL LKJ LKJ LK JL KJ
LKJK LJ LK J LKJ L 2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0
K 'WS 'ILJ [87 [09 I[8 U- 8 U- 8U -98 U - 98 [8 U -98 U [98 P

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2uWQKJH QLKJQNKL LKJ LKJ LK JL KJ
LKJK LJ LK J LKJ L 2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0
K 'WS 'ILJ [87 [09 I[8 U- 8 U- 8U -98 U - 98 [8 U -98 U [98 P

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))
pec=pet=7, y=10, c=2.5 da=0.1 r=0.5
initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2uWQKJH QLKJQNKL LKJ LKJ LK JL KJ
LKJK LJ LK J LKJ L 2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0
K 'WS 'ILJ [87 [09 I[8 U- 8 U- 8U -98 U - 98 [8 U -98 U [98 P

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2uWQKJH QLKJQNKL LKJ LKJ LK JL KJ
LKJK LJ LK J LKJ L 2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for tdu1/dt=(1/pec)*d2u1/dx2-


du1/dx-da*(1+u1)*exp(y*u2/(1+u2))
du2/dt=(1/pet)*d2u2/dx2-du2/dx+c*da*(1+u1)*exp(y*u2/(1+u2))

pec=pet=7, y=10, c=2.5 da=0.1 r=0.5


initial condition: u1=0, u2=0
boundary conditions at x=0, du1/dx=-pec*(r*ur(1)-r*ul(1)) and du2/dx=-pet*(r*ur(1)-
r*ul(1))
BC at x=1, du2/dx=0 and du2/dx=0

solve in the interval of 0 to 1 for x and 0 to 20 for t

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