Lecture 2 EE 743 Numerical Solution of Differential

Lecture 2 - EE 743 Numerical Solution of Differential Equations Professor: Ali Keyhani

Numerical Solution of Differential Equations n Euler’s Method 2

Numerical Solution of Differential Equations n Approximation by the Euler’s Method 3

Numerical Solution of Differential Equations 4

Numerical Solution of Differential Equations 5

Numerical Solution of Differential Equations n Trapezoidal Integration Method 6

Numerical Solution of Differential Equations 7

Numerical Solution of Differential Equations 8

Numerical Solution of Differential Equations n Trapezoidal Integration with Damping Method 9

Numerical Solution of Differential Equations n Problem: Use trapezoidal integration and compute the transient response of currents i 1 and i 2. 10

Numerical Solution of Differential Equations n Let 11

Numerical Solution of Differential Equations L p. X = R X + D U where L, X, R, D, and U are matrices or p. X=L-1 R X + L-1 D U Let A = L-1 R ; B = L-1 D 12

Numerical Solution of Differential Equations n Assuming the following values: – Rp=4 x 10 -5 ; Lp=6. 15 x 10 -5 H; Rs=3 x 10 -2 ; Ls=5. 3 x 10 -2 H; Show that, – n 13

Numerical Solution of Differential Equations n Let 14

Numerical Solution of Differential Equations n Selection of t: – Computation of eigenvalues of [A] l Recalling that 15

Numerical Solution of Differential Equations 16

Numerical Solution of Differential Equations n Trapezoidal Integration with Damping – Step 1: Predictor – Step 2: Corrector 17

Numerical Solution of Differential Equations n Predictor for n=0 18

Numerical Solution of Differential Equations n Corrector where, 19

Numerical Solution of Differential Equations n Predictor for n=1 20

Numerical Solution of Differential Equations n Corrector where, 21