High Order Difference Methods for Time Dependent PDE

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Focusing on finite difference methods (FDM), this book addresses gaps in the analysis of stability, accuracy, and effectiveness, particularly for higher-order methods where assumptions of smooth solutions and fine grids may not hold. It explores the challenges of constructing boundary conditions that maintain accuracy and stability, while also highlighting recent advancements in stable difference operators for initial-boundary value problems. The content balances theory with practical application, providing an overview of fundamental principles supplemented by simple model examples.