A general framework for solving differential equations
Luigi Brugnano, Felice Iavernaro
Abstract
Abstract Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) . Their derivation relies on the expansion of the vector field along a suitable orthonormal basis. Interestingly, this approach can be extended to cope with more general differential problems. In this paper we sketch this fact, by considering some relevant examples.
Topics & Concepts
SketchOrthonormal basisHamiltonian (control theory)Boundary value problemMathematicsApplied mathematicsDifferential equationComputer scienceMathematical analysisMathematical optimizationAlgorithmPhysicsQuantum mechanicsNumerical methods for differential equationsAdvanced Numerical Methods in Computational MathematicsMatrix Theory and Algorithms