determine-uk1-in-terms-of-ah-and-k-when-eulers-method-with-step-size-h-is-applie

Question

Determine uk+1u_{k+1} in terms of a,h,a,h, and kk when Euler’s method with step size hh is applied to the initial value problem y′(t)=$$at2y^{\prime}(t$$)=$$at^2$$, y(0)=1y(0)=1 with grid points tk=kht_k=kh and Euler approximations uku_k to y(tk)y(t_k).

Accepted Answer

uk+1=1+(k+1)(2k+1)6ah3k {\displaystyle\,u_{k+1}=1+\frac{(k+1)(2k+1)}{6}$$ah^3k$$\,}

Answer

uk+1=1+(k+1)2ah3k {\displaystyle\,u_{k+1}=1+\frac{(k+1)}{2}$$ah^3k$$\,}

Answer

uk+1=1+(k+1)(k+2)6ahk {\displaystyle\,u_{k+1}=1+\frac{(k+1)(k+2)}{6}ahk\,}

Answer

uk+1=(k+1)(k+2)6ah3k {{\displaystyle\,u_{k+1}=\frac{(k+1)(k+2)}{6}$$ah^3k$$\,}}

Determine uk+1u_{k+1} in terms of a,h,a,h, and kk when Euler’s method with step size hh is applied to the initial value problem y′(t)=at2y^{\(\prime\)}(t)=at^2, y(0)=1y(0)=1 with grid points tk=kht_k=kh and Euler approximations uku_k to y(tk)y(t_k).

Determine $u sub k plus 1$ in terms of $a, h,$ and $k$ when Euler’s method with step size $h$ is applied to the initial value problem $y^{'} (t) = a t^{2}$ , $y of 0 equals 1$ with grid points $t_{k} = k h$ and Euler approximations $u_{k}$ to $y (t_{k})$ .