Use Eulers method to solve dBdt008B with initial value B1200

Solution

It\'s not much difficult but just be careful in solving numericals.

here it is

dy/dt=f(y,t) y(0)=k

interval is [a,b]

then h=(b-a)/n

then it becomes n-step process .and it is observed that as n is increases more the precise the estimation will be 7 accurate the answer.

t_i =t_i-1 +h= a+ih

and

y_i=y_i-1+f(y_i-1,t_i-1)h

now we enter into our problem

dB/dt=0.08B

B₀=1200

A) 2 step method

t₀ =0

t=h=0.5

t1=0+0.5

=0.5

B₁=B₀+f(B₀,t0)h

=1200+(0.08*1200)0.5

=1200+48=1248

t₂=0.5+0.5=1

B₂=1248 +(0.08*1248)0.5

=1248+49.92

1297.92

therefore B(t2)=B(1)=1297.92

B) 4 step method

t₀ =0

t=h= 0.25

t1=0+0.25

=0.25

B₁=B₀+f(B₀,t0)h

=1200+(0.08*1200)0.25

=1200+24=1224

t₂=0.25+0.25=0.5

B₂=1224 +(0.08*1224)0.25

=1224+24.48

=1248.48

t₃=0.5+0.25=0.75

B₃=1248.48+(0.08*1248.48)0.25

=1248.48+24.97

=1273.45

t₄=0.75+.25=1

B₄=1273.45 +(0.08*1273.45)0.25

=1273.45+25.47

=1298.91

therefore B(t₄)=B(1)=1298.91