stuck in finite difference method

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Question:stuck in finite difference method

Posted: mostibra 20 Product: Maple

March 10 2017

i need to solve for u[i+1] as i attached i wrote the equations but i cant get any answers for it, the delta t is 0.1 and i need to go for ten steps, thank you

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for i from 0 to 10 do phat[i+1] := p[i+1]+187.9700000*u[i]+18.51050000*u__dot[i]+.4556*`u__ double dot`[i] end do

(14)

for i from 0 to 10 do u[i+1] := (1/18)*phat[i+1] end do;

(1/18)*p[2]+.5801543211*p[1]+109.0516077*u[0]+10.73894656*u__dot[0]+1.028361111*u__dot[1]+0.2531111111e-1*`u__ double dot`[1]

(1/18)*p[3]+.5801543211*p[2]+6.058422650*p[1]+1138.801706*u[0]+112.1444325*u__dot[0]+10.73894656*u__dot[1]+.2643183086*`u__ double dot`[1]+1.028361111*u__dot[2]+0.2531111111e-1*`u__ double dot`[2]

(1/18)*p[4]+.5801543211*p[3]+6.058422650*p[2]+63.26676144*p[1]+11892.25315*u[0]+1171.099388*u__dot[0]+112.1444325*u__dot[1]+2.760217359*`u__ double dot`[1]+10.73894656*u__dot[2]+.2643183086*`u__ double dot`[2]+1.028361111*u__dot[3]+0.2531111111e-1*`u__ double dot`[3]

(1/18)*p[5]+.5801543211*p[4]+6.058422650*p[3]+63.26676144*p[2]+660.6807306*p[1]+124188.1569*u[0]+12229.53067*u__dot[0]+1171.099388*u__dot[1]+28.82433650*`u__ double dot`[1]+112.1444325*u__dot[2]+2.760217359*`u__ double dot`[2]+10.73894656*u__dot[3]+.2643183086*`u__ double dot`[3]+1.028361111*u__dot[4]+0.2531111111e-1*`u__ double dot`[4]

(15)

for i from 0 to 10 do u__dot[i+1] := 2*u[i+1]/(.1)-u[i] end do;

1.111111111*p[3]+34.40000000*p[2]+1065.601376*p[1]+199664.3295*u[0]+19724.81428*u__dot[0]+15.67264000*`u__ double dot`[1]+.5062222222*`u__ double dot`[2]

1.111111111*p[4]+34.40000000*p[3]+1065.601376*p[2]+33008.92305*p[1]+6184962.451*u[0]+611011.6704*u__dot[0]+485.4879870*`u__ double dot`[1]+15.67264000*`u__ double dot`[2]+.5062222222*`u__ double dot`[3]

191590358.6*u[0]+15.67264000*`u__ double dot`[3]+.5062222222*`u__ double dot`[4]+15038.86535*`u__ double dot`[1]+485.4879870*`u__ double dot`[2]+18927187.66*u__dot[0]+1022510.881*p[1]+33008.92305*p[2]+1065.601376*p[3]+34.40000000*p[4]+1.111111111*p[5]

5934856645.*u[0]+485.4879870*`u__ double dot`[3]+15.67264000*`u__ double dot`[4]+.5062222222*`u__ double dot`[5]+465855.9575*`u__ double dot`[1]+15038.86535*`u__ double dot`[2]+586303748.8*u__dot[0]+31674117.34*p[1]+1022510.881*p[2]+33008.92305*p[3]+1065.601376*p[4]+34.40000000*p[5]+1.111111111*p[6]

0.1838428805e12*u[0]+15038.86535*`u__ double dot`[3]+485.4879870*`u__ double dot`[4]+15.67264000*`u__ double dot`[5]+.5062222222*`u__ double dot`[6]+14430727.85*`u__ double dot`[1]+465855.9575*`u__ double dot`[2]+0.1816181527e11*u__dot[0]+981162868.1*p[1]+31674117.34*p[2]+1022510.881*p[3]+33008.92305*p[4]+1065.601376*p[5]+34.40000000*p[6]+1.111111111*p[7]

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for i from 0 to 10 do `u__ double dot`[i+1] := 4*(u[i+1]-u[i])/.1^2-4*`u__ dot`[i+1]/(.1)-`u__ double dot`[i] end do;

22.22222222*p[2]+869.6543212*p[1]+159407.8005*u[0]+16097.73632*u__dot[0]-364.9777776*`u__ dot`[1]-40.00000000*`u__ dot`[2]

22.22222222*p[3]+869.6543212*p[2]+35344.36401*p[1]+6472746.341*u[0]+654241.8501*u__dot[0]-15483.60256*`u__ dot`[1]-364.9777776*`u__ dot`[2]-40.00000000*`u__ dot`[3]

-628632.0873*`u__ dot`[1]-15483.60256*`u__ dot`[2]-364.9777776*`u__ dot`[3]-40.00000000*`u__ dot`[4]+262941585.9*u[0]+26576866.06*u__dot[0]+1435772.456*p[1]+35344.36401*p[2]+869.6543212*p[3]+22.22222222*p[4]

-25536885.15*`u__ dot`[1]-628632.0873*`u__ dot`[2]-15483.60256*`u__ dot`[3]-364.9777776*`u__ dot`[4]-40.00000000*`u__ dot`[5]+0.1068138112e11*u[0]+1079622608.*u__dot[0]+58324875.48*p[1]+1435772.456*p[2]+35344.36401*p[3]+869.6543212*p[4]+22.22222222*p[5]

-1037375646.*`u__ dot`[1]-25536885.15*`u__ dot`[2]-628632.0873*`u__ dot`[3]-15483.60256*`u__ dot`[4]-364.9777776*`u__ dot`[5]-40.00000000*`u__ dot`[6]+0.4339059231e12*u[0]+0.4385712279e11*u__dot[0]+2369310541.*p[1]+58324875.48*p[2]+1435772.456*p[3]+35344.36401*p[4]+869.6543212*p[5]+22.22222222*p[6]

-0.4214093965e11*`u__ dot`[1]-1037375646.*`u__ dot`[2]-25536885.15*`u__ dot`[3]-628632.0873*`u__ dot`[4]-15483.60256*`u__ dot`[5]-364.9777776*`u__ dot`[6]-40.00000000*`u__ dot`[7]+0.1762640503e14*u[0]+0.1781592203e13*u__dot[0]+0.9624765415e11*p[1]+2369310541.*p[2]+58324875.48*p[3]+1435772.456*p[4]+35344.36401*p[5]+869.6543212*p[6]+22.22222222*p[7]

-0.1711876309e13*`u__ dot`[1]-0.4214093965e11*`u__ dot`[2]-1037375645.*`u__ dot`[3]-25536885.15*`u__ dot`[4]-628632.0873*`u__ dot`[5]-15483.60256*`u__ dot`[6]-364.9777776*`u__ dot`[7]-40.00000000*`u__ dot`[8]+0.7160311434e15*u[0]+0.7237298245e14*u__dot[0]+0.3909834009e13*p[1]+0.9624765415e11*p[2]+2369310541.*p[3]+58324875.48*p[4]+1435772.456*p[5]+35344.36401*p[6]+869.6543212*p[7]+22.22222222*p[8]

(17)

$slon := fsolve({0, p[11]+187.9700000*u[10]+18.51050000*u__dot[10]+.4556*`u__ double dot`[10], 0.1692751266e18*u[0]+0.1384718205e11*`u__ double dot`[3]+447017802.5*`u__ double dot`[4]+14430727.85*`u__ double dot`[5]+465855.9575*`u__ double dot`[6]+15038.86535*`u__ double dot`[7]+485.4879870*`u__ double dot`[8]+15.67264000*`u__ double dot`[9]+.5062222222*`u__ double dot`[10]+0.1328723353e14*`u__ double dot`[1]+0.4289414197e12*`u__ double dot`[2]+0.1672266869e17*u__dot[0]+1065.601376*p[9]+34.40000000*p[10]+1.111111111*p[11]+0.9034152876e15*p[1]+0.2916425269e14*p[2]+0.9414868743e12*p[3]+0.3039328810e11*p[4]+981162868.3*p[5]+31674117.34*p[6]+1022510.881*p[7]+33008.92305*p[8], -0.1147563911e18*`u__ dot`[1]-0.2824936664e16*`u__ dot`[2]-0.6954093867e14*`u__ dot`[3]-0.1711876310e13*`u__ dot`[4]-0.4214093965e11*`u__ dot`[5]-1037375646.*`u__ dot`[6]-25536885.15*`u__ dot`[7]-628632.0873*`u__ dot`[8]-15483.60256*`u__ dot`[9]-364.9777776*`u__ dot`[10]-40.00000000*`u__ dot`[11]+0.4799946674e20*u[0]+0.4851555123e19*u__dot[0]+35344.36401*p[9]+869.6543212*p[10]+22.22222222*p[11]+0.2620974648e18*p[1]+0.6452004379e16*p[2]+0.1588277877e15*p[3]+0.3909834009e13*p[4]+0.9624765415e11*p[5]+2369310540.*p[6]+58324875.44*p[7]+1435772.456*p[8], 0.1610558112e12*u[0]+342786.3064*`u__ double dot`[3]+32825.20357*`u__ double dot`[4]+3143.340237*`u__ double dot`[5]+301.0061407*`u__ double dot`[6]+28.82433650*`u__ double dot`[7]+2.760217359*`u__ double dot`[8]+.2643183086*`u__ double dot`[9]+0.2531111111e-1*`u__ double dot`[10]+37381397.82*`u__ double dot`[1]+3579641.223*`u__ double dot`[2]+1518762873.*u__dot[1]+145436674.5*u__dot[2]+13927010.38*u__dot[3]+1333649.981*u__dot[4]+127710.2711*u__dot[5]+12229.53067*u__dot[6]+1171.099388*u__dot[7]+112.1444325*u__dot[8]+10.73894656*u__dot[9]+1.028361111*u__dot[10]+0.1586010318e11*u__dot[0]+6.058422650*p[9]+.5801543211*p[10]+(1/18)*p[11]+856816572.8*p[1]+82048722.17*p[2]+7856982.494*p[3]+752384.3428*p[4]+72048.29583*p[5]+6899.342050*p[6]+660.6807306*p[7]+63.26676144*p[8]});$

${p[1] = 0.2999999998e-1*`u__ dot`[2]+0.9374999995e-13*`u__ dot`[3]-0.1499999999e-4*`u__ dot`[4]+0.1312499999e-15*`u__ dot`[5]+0.4999999999e-8*`u__ dot`[6]-0.6999999938e-9*`u__ dot`[7]+0.9899999882e-9*`u__ dot`[8]-0.1827374978e-8*`u__ dot`[9]+0.3743087460e-8*`u__ dot`[10]+0.7499999993e-16*`u__ dot`[11]+0.4597499946e-10*p[9]-0.1051124990e-9*p[10]-0.2053929019e-9*p[11]-0.2499999999e-1*p[2]-0.2499999998e-3*p[3]-0.2499999999e-4*p[4]-0.2499999999e-6*p[5]-0.5000000000e-8*p[6]-0.9999999992e-9*p[7]-0.3749999970e-10*p[8], p[2] = p[2], p[3] = p[3], p[4] = p[4], p[5] = p[5], p[6] = p[6], p[7] = p[7], p[8] = p[8], p[9] = p[9], p[10] = p[10], p[11] = p[11], u[0] = 0.281894999e-4*`u__ dot`[2]+0.7830419785e-6*`u__ dot`[3]+0.318079236e-8*`u__ dot`[4]+0.9022187373e-9*`u__ dot`[5]-0.1628286346e-10*`u__ dot`[6]+0.1100239238e-9*`u__ dot`[7]-0.2048575058e-9*`u__ dot`[8]+0.3826992048e-9*`u__ dot`[9]-0.7123420880e-9*`u__ dot`[10]+0.1380032829e-8*`u__ dot`[11]-0.9758339382e-11*p[9]+0.1808837852e-10*p[10]-0.3663799046e-10*p[11]-0.989828263e-4*p[2]-0.884545513e-6*p[3]-0.8052117590e-7*p[4]-0.1650827489e-8*p[5]-0.2205906206e-10*p[6]-0.3199234662e-11*p[7]+0.5195642082e-11*p[8], `u__ dot`[1] = -0.4999999998e-1*`u__ dot`[2]+0.2499999997e-3*`u__ dot`[3]+0.4999999998e-5*`u__ dot`[4]+0.7499999995e-6*`u__ dot`[5]-0.1499999999e-7*`u__ dot`[6]+0.7949999997e-7*`u__ dot`[7]-0.1479199999e-6*`u__ dot`[8]+0.2763269999e-6*`u__ dot`[9]-0.5141608198e-6*`u__ dot`[10]+0.9999999996e-6*`u__ dot`[11]-0.7045749997e-8*p[9]+0.1305056749e-7*p[10]-0.2665930549e-7*p[11]+0.1499999999e-2*p[3]-0.2499999999e-4*p[4]-0.9999999996e-9*p[7]+0.3769999998e-8*p[8], `u__ dot`[2] = `u__ dot`[2], `u__ dot`[3] = `u__ dot`[3], `u__ dot`[4] = `u__ dot`[4], `u__ dot`[5] = `u__ dot`[5], `u__ dot`[6] = `u__ dot`[6], `u__ dot`[7] = `u__ dot`[7], `u__ dot`[8] = `u__ dot`[8], `u__ dot`[9] = `u__ dot`[9], `u__ dot`[10] = `u__ dot`[10], `u__ dot`[11] = `u__ dot`[11], u__dot[0] = -0.2499999998e-2*`u__ dot`[2]+0.1249999999e-4*`u__ dot`[3]+0.1249999999e-5*`u__ dot`[4]+0.1749999998e-7*`u__ dot`[5]-0.2499999998e-9*`u__ dot`[6]+0.8349999992e-9*`u__ dot`[7]-0.1525399998e-8*`u__ dot`[8]+0.2848549998e-8*`u__ dot`[9]-0.5316285694e-8*`u__ dot`[10]+0.9999999990e-8*`u__ dot`[11]-0.7260249992e-10*p[9]+0.1354106748e-9*p[10]-0.2570080548e-9*p[11]+0.9999999994e-3*p[2]+0.2499999997e-4*p[3]+0.7499999994e-6*p[4]+0.9999999994e-8*p[5]+0.4999999995e-10*p[7]+0.3949999996e-10*p[8]}$

(18)

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