document: Adaptive multiresolution approach for solution of hyperbolic PDEs This paper establishes an innovative and efficient multiresolution adaptive approach combined with high-resolution methods , for the numerical solution of a single or a system of partial differential equations . The proposed methodology is unconditionally bounded -LRB- even for hyperbolic equations -RRB- and dynamically adapts the grid so that higher spatial resolution is automatically allocated to domain regions where strong gradients are observed , thus possessing the two desired properties of a numerical approach : stability and accuracy . Numerical results for five test problems are presented which clearly show the robustness and cost effectiveness of the proposed method
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