Functionally-fitted block methods for ordinary differential equations

Computer methods for ordinary differential equations and differential-algebraic equations

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General linear methods for ordinary differential equations

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Exponential-Krylov methods for ordinary differential equations

This paper develops a new class of exponential-type integrators where all the matrix exponentiations are performed in a single Krylov space of low dimension. The new family, called Lightly Implicit KrylovExponential (LIKE), is well suited for solving large scale systems of ODEs or semi-discrete PDEs. The time discretization and the Krylov space approximation are treated as a single computationa...

Numerical Methods for Ordinary Differential Equations

2 – Block 3 - Point Modified Numerov Block Methods for Solving Ordinary Differential Equations

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ f x, y , a x b with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids...