Explicit finite difference schemes adapted to advection-reaction equations
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
On the numerical solution of the heat conduction equations subject to nonlocal conditions
Applied Numerical Mathematics
A 17th-order Radau IIA method for package RADAU. Applications in mechanical systems
Computers & Mathematics with Applications
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We present BDF type formulas of high-order (4, 5 and 6), capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential with parameter A and ordinary polynomials. For A = 0, the new formulas reduce to the classical BDF formulas. Theorems of the local truncation error reveal the good behavior of the new methods with stiff problems. Plots of their 0-stability regions in terms of the eigenvalues of the parameter A h are provided. Plots of their absolute stability regions that include the whole of the negative real axis are provided. The weights of the method usually require the evaluation of a matrix exponential. However, if the dimension of the matrix is large, we shall not perform this calculus and shall only approximate those coefficients once. Numerical examples underscore the efficiency of the proposed codes, especially when one is integrating stiff oscillatory problems.