The usage of terms 'initial value' and 'boundary value' is a massive failure of mathematics education.
'Initial' refers to time-like variables, and 'boundary' refers to space-like variables.
There is no notion of time in mathematics. There is only a notion of space, due to geometry. I had the longest time coming to grips with the question, "mathematically what is the difference between initial value and boundary value?" only to realize the distinction is meaningless in mathematics. It's a relic of the past when differential equations were studied under physics, where time and space are a huge part of the conceptual foundation.
Sometimes I wonder how much progress we would make in education if we didn't confuse the heck of our students in the name of convention and historical baggage.
Since time is 1D while space may have more dimensions, initial values are connected to ODEs while boundary ones with PDEs. Their behavior is quite different.
'Initial' refers to time-like variables, and 'boundary' refers to space-like variables.
There is no notion of time in mathematics. There is only a notion of space, due to geometry. I had the longest time coming to grips with the question, "mathematically what is the difference between initial value and boundary value?" only to realize the distinction is meaningless in mathematics. It's a relic of the past when differential equations were studied under physics, where time and space are a huge part of the conceptual foundation.
Sometimes I wonder how much progress we would make in education if we didn't confuse the heck of our students in the name of convention and historical baggage.