- Show Local Truncation Error Given Y Def Dy Dt F Y And The Following Numerical Integration Formula Vi 1 Ki 1 1 (314.84 KiB) Viewed 47 times
Show Local Truncation Error Given y' def dy/dt = f(y) and the following numerical integration formula: = = Vi+1 = Ķi-1 +
-
answerhappygod
- Site Admin
- Posts: 899604
- Joined: Mon Aug 02, 2021 8:13 am
Show Local Truncation Error Given y' def dy/dt = f(y) and the following numerical integration formula: = = Vi+1 = Ķi-1 +
Show Local Truncation Error Given y' def dy/dt = f(y) and the following numerical integration formula: = = Vi+1 = Ķi-1 + 2hf (ſi) apply Taylor's formula to show LTE is: Ģi+1 – y(ti+h) = 0(h3). = h2 = Use the following assumptions/hints: . True solution Taylor series: ylti +n) = y(tj) + hy'(tj) + *y"(tj) + Och3) ) + ( • Assume exact values for: ſi-1= y(ti – h), Ķi = y(ti) Taylor series for: y(ti – h) = y(t;) – hy'(t;) +y"(ti) + 0(h3) • It is not necessary to expand derivatives of y, y',y" in terms of f. - = h2 1 = 2
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!