@Markiyan Hirnyk 

q(x,t)=1000

@Carl Love 

tnx my friend,i have data in a file excell(attach in below) and i will import them to maple and plot the figure,how do this work?

with regards...

data.xls

@Carl Love 

I saw that in a site,maybe that is wrong,how can i increase accuracy of rosenbrock method?

@Carl Love 

thanks,can i increase accuracy of rosenbrock numerical method in maple?this method default it uses a relative tolerance of 10^-3,can i make this method with tolerance of 10^-6?
with regards.........

@Carl Love 

very thank you,you solve my problem,i dont understand operand positions within the piecewise expression 2 and 4?always take values 2 and 4 or get other values?

@Carl Love 

tank you so much my friend,can you help me to solve the five nonlinear odes with numerical method?

EQ1 := -9.034666667*10^5*Pi^2*q3(t)*q1(t)+3044.230933*Pi*q1(t)*q5(t)+3044.230933*Pi*q1(t)*q4(t)+2.541000000*10^5*q1(t)^3*Pi^4+2.171794873*10^5*q1(t)*Pi^2-2.171794873*10^5*q2(t)*Pi+4.372778665*(diff(q1(t), t, t))

EQ2 := 1.093194666*q2(t)*Pi^2-54294.87180*q1(t)*Pi+0.7054749580e-5*(diff(q2(t), t, t))-.8371635069*q4(t)*Pi+54294.87180*q2(t)+.8371635069*q5(t)*Pi

EQ3 := 9.034666667*10^5*q1(t)^2*Pi^2+6.776000000*10^5*Pi^2*q3(t)-2283.173200*q5(t)*Pi+4.372778667*(diff(q3(t), t, t))-2283.173200*q4(t)*Pi

EQ4 := piecewise(t < 10, .5000000000-525.9936000*q5(t)*Pi^2-2.035463170*10^7*(diff(q4(t), t))-.5000000000*t-2.035463170*10^7*(diff(q5(t), t))-525.9936000*q4(t)*Pi^2, 10 <= t, -2.035463170*10^7*(diff(q4(t), t))-525.9936000*q4(t)*Pi^2-2.035463170*10^7*(diff(q5(t), t))-525.9936000*q5(t)*Pi^2)

EQ5 := piecewise(t < 10, 0.5500000000e-3+.1928643200*q5(t)*Pi^2-7463.364955*(diff(q4(t), t))+29886.00000*q5(t)-0.5500000000e-3*t+7463.364955*(diff(q5(t), t))-.1928643200*q4(t)*Pi^2-29886.00000*q4(t), 10 <= t, .1928643200*q5(t)*Pi^2-29886.00000*q4(t)+29886.00000*q5(t)-.1928643200*q4(t)*Pi^2-7463.364955*(diff(q4(t), t))+7463.364955*(diff(q5(t), t)))

initial conditions are zero.

@nm 

no my friend,i define function f(x,t) true,in terms of piecewise:

f := (x, t) -> piecewise(t < 10, 0.480e9*(1-(1/10)*t)*sin(Pi*x), 10 < t, 0)

@Carl Love 

excuse me my friend,my before question is wrong,my function in this case is:

f(x,t)=(1-t)*sin(Pi*x) for t<10 and 0 for t>10

eq1 := diff(y(t), t, t)-y(t)^2-f(x,t) = 0
eq2 :=simplify( int(lhs(eq1)*sin(Pi*x), x = 0 .. 1) = 0)

when use the dsolve i see error,why?

initial conditions are zero.

@Carl Love 

tnx my friend,infact i will solve the ode result of below eq2:

f:= t-> piecewise(t < 10, 1-t, t):
eq1 := diff(y(t), t, t)-y(t)^2-f(t) = 0
eq2 := int(lhs(eq1)*sin(Pi*x), x = 0 .. 1) = 0
how?

initial conditions are zero.

@Carl Love 

tnx,how solve the nonlinear ode with numerical method?

diff(y(t), t, t)-y(t)^2 = f(t)

f(t)=1-t for 0<t<10 and t for t>10

initial conditions are zero.