Efficient Solution of Multi-Term Fractional Differential Equations Using P(EC) m E Methods

摘要: We investigate strategies for the numerical solution of initial value problem y(αv)(x) = f(x, y(x), y(α1)(x),..., y(αv-1)(x)) with conditions y(k)(0) y0(k) (k 0, 1,..., ⌈αv⌉ - 1), where 0 (not necessarily αj ∈ N) in sense Caputo. The methods are based on integration techniques applied to an equivalent nonlinear and weakly singular Volterra integral equation. classical approach leads algorithm very high arithmetic complexity. Therefore we derive alternative that lower complexity without sacrificing too much precision.