numerical solution for initial value problem numerical analysis

Download Numerical Solution for Initial Value Problem Numerical Analysis

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Numerical Solution for Initial Value Problem Numerical Analysis Slide 2 Introduction x0x0 x1x1 x2x2 x3x3 xnxn Slide 3 Well-posed Problem Slide 4 Well-posed Formula: Example Slide 5 Classes of Methods Slide 6 Slide 7 Euler Method Slide 8 Slide 9 Euler Method: Formula Slide 10 Euler Method: Geometry Meaning Slide 11 Euler Method: Example Slide 12 Slide 13 Taylor order n Slide 14 Taylor order n: Formula Slide 15 Taylor order n: Example Slide 16 Slide 17 Slide 18 Slide 19 Slide 20 Slide 21 Slide 22 Interpolate other values Slide 23 Slide 24 Slide 25 Runge-Kutta Method (RK) Runge-Kutta 25 Slide 26 Taylor Theory in 2 Variables 26 Slide 27 Runge-Kutta order 2 27 Slide 28 Runge-Kutta order 2 28 Slide 29 Runge-Kutta order 2 29 Slide 30 Runge-Kutta order 2 30 Slide 31 RK2: Midpoint Formula 31 Slide 32 RK2: Modified Euler Formula 32 Slide 33 RK2: Heuns Formula 33 Slide 34 RK2: Example 34 Slide 35 RK2: Example 35 Slide 36 RK2: Example 36 Slide 37 RK2: Example 37 Slide 38 RK2: Example 38 Slide 39 Runge-Kutta order 4 39 Slide 40 RK4: Example 40 Slide 41 RK4: Example 41 Slide 42 RK4: Example 42 Slide 43 RK4: Example 43 Slide 44 RK4: Example 44 Slide 45 RK4 vs Other Methods 45 Slide 46 RK4 vs Other Methods 46 Slide 47 RK4 vs Other Methods 47 Slide 48 Multi-Step Method 48 Slide 49 Multi-Step Method 49 Slide 50 Multi-Step Method: Explicit case 50 Slide 51 Adams-Bashforth Formula 51 Slide 52 Multi-Step Method: Explicit case 52 Slide 53 Multi-Step Method: Explicit case 53 Slide 54 Multi-Step Method: Implicit case 54 Slide 55 Multi-Step Method: Implicit case 55 Slide 56 Predictor-Corrector Method 2 (Predictor Formula) (Corrector Formula) (inner iteration) 56 Slide 57 Predictor-Corrector Method 57 Slide 58 Predictor-Corrector Method 58 Slide 59 Predictor-Corrector Method: Example 59 Slide 60 Predictor-Corrector Method: Example 60 Slide 61 Predictor-Corrector Method: Example 61 Slide 62 Predictor-Corrector Method: Example 62 Slide 63 Predictor-Corrector Method: Example 63 Slide 64 High ODE and System of ODE Slide 65 Slide 66 Slide 67 Slide 68 RK4 in vector form Slide 69 ABM4 in vector form Slide 70 High ODE and System of ODE: Example Slide 71 Slide 72 Slide 73 Slide 74 Slide 75 Slide 76 Slide 77 Slide 78 Slide 79 Divided Different Method for BVP Slide 80 Differential Equation to Divided Different Form Slide 81 Divided Different Formula for Linear BVP Slide 82 Existing of Solution Slide 83 Divided Different for BVP: Example Slide 84 Slide 85

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