Visualitzar TFG

Visualitzar TFG

Tabla de Contenidos: “…3.4.1 Thomas Algorithm for Tridiagonal Systems -- 3.4.2 Crank-Nicholson Scheme: Truncation Error, Consistency, and Convergence -- 3.4.3 Dissipative and Dispersive Errors -- 3.4.4 Stability of the Crank-Nicholson Scheme -- 3.5 A Note on Implicit Methods -- 3.6 Leap-frog and DuFort-Frankel Schemes -- 3.6.1 Truncation Error of the DuFort-Frankel Scheme -- 3.6.2 Stability of DuFort-Frankel Scheme -- 3.7 Operator Notation -- 3.8 The Alternating Direction Implicit (ADI) Method -- 3.8.1 ADI Scheme -- 3.8.2 Splitting and Approximate Factorisation -- 3.8.3 Stability of the ADI Scheme -- 3.8.4 Program 3.1: adi.f -- 3.9 Summary -- 3.10 Key Terms -- 3.11 Exercise 3 -- Chapter 4: Equations of Hyperbolic Type -- 4.1 Introduction -- 4.2 Explicit Schemes -- 4.2.1 FTCS Scheme -- 4.2.2 FTFS Scheme -- 4.2.3 Upwind Scheme: First Order -- 4.2.4 Upwind Scheme: Modified Equation -- 4.2.5 The Lax Scheme -- 4.2.6 Consistency of Lax Scheme -- 4.2.7 Lax Scheme: Modified Equation -- 4.2.8 The Leap-Frog Scheme -- 4.3 Lax-Wendroff Scheme and Variants -- 4.3.1 Lax-Wendroff Scheme: Modified Equation -- 4.3.2 Two-Step Lax-Wendroff Scheme -- 4.3.3 The MacCormack Scheme -- 4.3.4 Upwind Scheme: Warming-Beam -- 4.4 Implicit Schemes -- 4.5 More on Upwind Schemes -- 4.6 Scalar Conservation Law: Lax-Wendroff and Related Schemes -- 4.6.1 Program 4.1: Ixmc.f -- 4.6.2 Implicit Schemes for Scalar Conservation Law -- 4.7 Hyperbolic System of Conservation Laws -- 4.7.1 System of Conservation Laws -- 4.8 Second-order Wave Equation -- 4.8.1 Stability of the Leap-Frog Scheme for the Wave Equation -- 4.8.2 An Implicit Scheme for the Second-Order Wave Equation -- 4.8.3 Stability of the Implicit Scheme -- 4.9 Method of Characteristics for Second-order Hyperbolic Equations -- 4.10 Model Convection-Diffusion Equation -- 4.10.1 Steady Convection-Diffusion Equation…”