BDF a BBDF pro řešení diferenciálních rovnic

Abstract

his thesis explores the Backward Differentiation Formula (BDF) and Block Backward Differentiation Formula (BBDF) methods for solving stiff ordinary differential equations (ODEs). BDF methods are known for their stability, which makes them effective for stiff problems, while BBDF methods enhance this by solving multiple steps simultaneously, improving both efficiency and stability. The research delves into the derivation, implementation, and analysis of these methods, with a focus on their stability and convergence characteristics. We derive BDF and BBDF methods from fundamental principles, Stability analysis is conducted using techniques such as the root locus method and stability region characterization. Numerical experiments are conducted to validate the theoretical findings, comparing the performance of BDF and BBDF methods of several variants . The results demonstrate the better stability and efficiency of BBDF methods in solving ODEs, . This work offers a comprehensive study of BDF and BBDF methods, providing insights into their practical applications and potential for further development.his thesis explores the Backward Differentiation Formula (BDF) and Block Backward Differentiation Formula (BBDF) methods for solving stiff ordinary differential equations (ODEs). BDF methods are known for their stability, which makes them effective for stiff problems, while BBDF methods enhance this by solving multiple steps simultaneously, improving both efficiency and stability. The research delves into the derivation, implementation, and analysis of these methods, with a focus on their stability and convergence characteristics. We derive BDF and BBDF methods from fundamental principles, Stability analysis is conducted using techniques such as the root locus method and stability region characterization. Numerical experiments are conducted to validate the theoretical findings, comparing the performance of BDF and BBDF methods of several variants . The results demonstrate the better stability and efficiency of BBDF methods in solving ODEs, . This work offers a comprehensive study of BDF and BBDF methods, providing insights into their practical applications and potential for further development.