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I have the system of PDE below and I want to solve it using finite difference method but I think I have to reduce it first to a system of first order PDE. The problem is that I don't know how to reduce this PDE to a first order system. I will appreciate any hints in this regard. Thanks

∇^{6}w_{1}+ μ_{1}∂/∂t(∇^{4}w_{1}) + μ_{2}∂^{2}/∂t^{2}(∇^{2}w_{1}) + μ_{3}∇^{4}w_{1}+ μ_{4}∂^{3}w_{1}/∂t^{3}+ μ_{5}∂/∂t(∇^{2}w_{2}) + μ_{6}∇^{2}w_{2}= g_{1}(x, y, t)

∇^{6}w_{2}+ χ_{1}∂/∂t(∇^{4}w_{2}) + χ_{2}∂^{2}/∂t^{2}(∇^{2}w_{2}) + χ_{3}∇^{4}w_{2}+ χ_{4}∂^{3}w_{2}/∂t^{3}+ χ_{5}∂/∂t(∇^{2}w_{1}) + χ_{6}∇^{4}w_{1}= g_{2}(x, y, t)

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# How to reduce higher order partial differential equations

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